Package 'cascsim'

Title: Casualty Actuarial Society Individual Claim Simulator
Description: It is an open source insurance claim simulation engine sponsored by the Casualty Actuarial Society. It generates individual insurance claims including open claims, reopened claims, incurred but not reported claims and future claims. It also includes claim data fitting functions to help set simulation assumptions. It is useful for claim level reserving analysis. Parodi (2013) <https://www.actuaries.org.uk/documents/triangle-free-reserving-non-traditional-framework-estimating-reserves-and-reserve-uncertainty>.
Authors: Robert Bear [aut], Kailan Shang [aut, cre], Hai You [aut], Brian Fannin [ctb]
Maintainer: Kailan Shang <[email protected]>
License: GPL-3
Version: 0.4
Built: 2024-11-19 03:55:09 UTC
Source: https://github.com/cran/cascsim

Help Index

Plotting the CDF of data and fitted distribution

Description

Plotting the CDF of data and fitted distribution

Usage

CDFPlot(object, ...)

## S4 method for signature 'FitDist'
CDFPlot(object, n = missing)

Arguments

object

FitDist Object
...

Additional function arguments
n

Number of samples, should not be used in current setting

Examples

library(cascsim)
data(claimdata)

#frequecy fitting example
findex <- new("Index", startDate = as.Date("2012-01-01"), tabulate=TRUE, monthlyIndex = c(rep(1,11),
cumprod(c(1,rep(1.5^(1/12),11))),cumprod(c(1.5,rep((1.3/1.5)^(1/12),11))),
cumprod(c(1.3,rep((1.35/1.3)^(1/12),11))),cumprod(c(1.35,rep((1.4/1.35)^(1/12),11))),1.4))
rawdata <- as.data.frame(as.Date(claimdata[(claimdata[,"LoB"]=="Auto" & 
claimdata[,"Type"]=="H"),]$occurrenceDate))
colnames(rawdata)<-"occurrenceDate"
xFit <- new("FitDist", observation=rawdata, trend=findex,startDate = as.Date("2012-01-01"),
method="mle",ifreq=TRUE,idate=TRUE, freq="Monthly")
xFit <- setFitdata(xFit)
setTrialDist(xFit) <- new("Poisson")
xFit@soutput
CDFPlot(xFit)

Chi-Squared Test

Description

Chi-Squared Test

Usage

ChiSqrTest(object, ...)

## S4 method for signature 'FitDist'
ChiSqrTest(object)

Arguments

object

FitDist Object
...

Additional function arguments

Sample Claim Data

Description

A dataset containing about 10,000 simulated claim records from 2012 to 2016 for illustration. The variables are as follows:

Usage

data(claimdata)

Format

A data frame with 10030 rows and 15 variables

Details

  • ClaimID. Claim ID

  • LoB. Line of Business (Auto, Liab, Property)

  • Type. Claim Type (N: Normal, H: High)

  • status. Current Claim Status (Closed, Open)

  • occurrenceDate. Claim Occurrence Date

  • reportDate. Claim Report Date

  • incurredLoss. Incurred Loss. For closed claim, it is the ultimate loss. For open claim, it is the estimated or booked loss.

  • osRatio. Outstanding Ratio

  • settlementDate. Claim Settlement Date.

  • Paid. Paid Loss by the valuation date. It equals incurredLoss * (1-osRatio)

  • totalLoss. Total loss before deductible and limit. If not available, it will be set as incurredLoss and not used for fitting.

  • Deductible. Deductible applied to the claim.

  • Limit. Limit applied to the claim.

  • LAE. Loss adjustment expense at the claim level. It can be omitted if idemnity and LAE are modeled together as incurred loss.

  • claimLiability. Indicating whether the claim is invalid and leads to zero payment. It excludes valid claims that are smaller than deductibles.

Claim data fitting analysis at line/type/status level

Description

Claim data fitting analysis at line/type/status level

Usage

claimFitting(object, claimData, ...)

## S4 method for signature 'Simulation,data.frame'
claimFitting(object, claimData,
  startDate = as.Date("2012-01-01"),
  evaluationDate = as.Date("2016-12-31"), lineList = object@lines,
  typeList = object@types, discreteDist = c("Poisson",
  "NegativeBinomial", "Geometric"), continuousDist = c("Normal",
  "Lognormal", "Pareto", "Weibull", "Gamma", "Uniform", "Exponential"),
  copulaList = c("normal"), fReportLag = TRUE, fSettlementLag = TRUE,
  fFrequency = TRUE, fSeverity = TRUE, fSSRCorrelation = TRUE,
  fFreqCorrelation = TRUE, copulaTest = TRUE, iTotalLoss = TRUE,
  fDeductible = TRUE, fLimit = TRUE, check = TRUE)

Arguments

object

Simulation object
claimData

claim data including existing claims for RBNER and claim reopenness analysis
...

Additional parameters that may or may not be used.
startDate

Date after which claims are analyzed;
evaluationDate

Date of evaluation for existing claims and IBNR;
lineList

List of business lines to be included in claim fitting;
typeList

List of claim types to be included in claim fitting;
discreteDist

List of discrete distributions to try fitting (report lag, settlemet lag, frequency);
continuousDist

List of continuous distribution to try fitting (severity);
copulaList

List of copula to try fitting;
fReportLag

Boolean variable to indicate whether report lag needs to be fitted;
fSettlementLag

Boolean variable to indicate whether settlement lag needs to be fitted;
fFrequency

Boolean variable to indicate whether monthly frequency needs to be fitted;
fSeverity

Boolean variable to indicate whether severity needs to be fitted;
fSSRCorrelation

Boolean variable to indicate whether copula among severity, report lag and settlement lag needs to be fitted;
fFreqCorrelation

Boolean variable to indicate whether copula among frequencies of business lines needs to be fitted.
copulaTest

Whether to test copula. The testing could take a very long time;
iTotalLoss

Boolean variable to indicate whether total loss before deductible and limit is available for severity fitting;
fDeductible

Boolean variable to indicate whether deductible empirical distribution needs to be fitted;
fLimit

Boolean variable to indicate whether limit empirical distribution needs to be fitted;
check

Boolean variable to indicate whether graph of each tried distribution fitting needs to be generated and saved.

Examples

library(cascsim)
data(claimdata)
lines<-c("Auto")
types<-c("N")
#exposure index
index1 <- new("Index",monthlyIndex=c(rep(1,11),cumprod(c(1,rep(1.5^(1/12),11))),
cumprod(c(1.5,rep((1.3/1.5)^(1/12),11))),
cumprod(c(1.3,rep((1.35/1.3)^(1/12),11))),cumprod(c(1.35,rep((1.4/1.35)^(1/12),11))),rep(1.4,301)))
#severity index
index2 <- new("Index",monthlyIndex=c(cumprod(c(1,rep(1.03^(1/12),59))),rep(1.03^(5),300)))
objan <- new("ClaimType", line="Auto",claimType="N",exposureIndex=index1,severityIndex=index2)
objlist <- list(objan)
simobj <- new("Simulation",lines=lines,types=types,claimobjs=objlist,iFit=TRUE,
iCopula=FALSE, iReport=TRUE, workingFolder=tempdir())
simobj <- claimFitting(simobj,claimdata,fSSRCorrelation = FALSE, fSettlementLag = FALSE)

Claim simulation at line/type/status level

Description

Claim simulation at line/type/status level

Usage

claimSample(object, ...)

## S4 method for signature 'ClaimType'
claimSample(object, claimData = data.frame(),
  startDate = as.Date("2012-01-01"),
  evaluationDate = as.Date("2016-12-31"))

Arguments

object

ClaimType object
...

Additional parameters that may or may not be used.
claimData

claim data including existing claims for RBNER and claim reopenness analysis;
startDate

Date from which claim data is included in the analysis;
evaluationDate

Date of evaluation.

Examples

#run time is about 12s(>10s) and is commented out here to avoid long waiting time
#library(cascsim)
#data(claimdata)
##IBNR simulation
#claimobj <- new("ClaimType", line="Auto",claimType="N",iRBNER=FALSE,iROPEN=FALSE,
#iIBNR=TRUE,iUPR=FALSE,
#IBNRfreqIndex=new("Index",startDate=as.Date("2016-01-01"),
#monthlyIndex=rep(30,12)),iCopula=TRUE)
#ibnrdata <- claimSample(claimobj,claimdata)
#ibnrdata

Claim simulation at line/type/status level

Description

Claim simulation at line/type/status level

Usage

claimSimulation(object, ...)

## S4 method for signature 'Simulation'
claimSimulation(object, claimData = data.frame(),
  startDate = as.Date("2012-01-01"),
  evaluationDate = as.Date("2016-12-31"),
  futureDate = as.Date("2017-12-31"), append = TRUE)

Arguments

object

Simulation object
...

Additional parameters that may or may not be used.
claimData

claim data including existing claims for RBNER and claim reopenness analysis;
startDate

Date after which claims are analyzed;
evaluationDate

Date of evaluation for existing claims and IBNR;
futureDate

Date of evaluation for UPR (future claims).
append

Boolean variable to indicate whether existing simulation results need to be kept.

Examples

library(cascsim)
data(claimdata)
lines <- c("Auto")
types <- c("N")
AutoN <- new("ClaimType", line = "Auto", claimType = "N")
AutoN@exposureIndex <- setIndex(new("Index",indexID="I1",tabulate= FALSE,
startDate=as.Date("2012-01-01"), annualizedRate = 0)) # level exposure across time
AutoN@frequency <- new("Poisson", p1 =50)
AutoN@severityIndex <- setIndex(new("Index",indexID="I2",tabulate= FALSE,
startDate=as.Date("2012-01-01"), annualizedRate = 0.02)) #assuming a 2% annual inflation
AutoN@severity <- new("Lognormal", p1 =2, p2 =3)
AutoN@deductible <- new("Empirical", empirical=matrix(c(0,1,100,100),2,2))
AutoN@limit <- new("Empirical", empirical=matrix(c(0,1,1e8,1e8),2,2))
AutoN@p0<-new("DevFac",meanList=c(0,0),volList=c(0,0))
AutoN@reportLag <- new("Exponential", p1 =0.1)
AutoN@settlementLag <- new("Exponential", p1 =0.05)
AutoN@iCopula <- TRUE #use copula
AutoN@ssrCopula <- new("CopulaObj", type ="normal", dimension = 3, 
param = c(0.1,0.2,0.1))#A Gaussian Copula
AutoN@ssrCopula@marginal <- c(AutoN@severity,AutoN@settlementLag,AutoN@reportLag)
AutoN@laeDevFac <- new("DevFac",FacID="F1",FacModel= TRUE,fun="linear",
paras =c(5,1.5,0.005,1.2,3))
AutoN@fIBNER <- new("DevFac",FacID="D1",FacModel= FALSE,
meanList =c(1.2,1.15,1.1,1.05,1),volList =c(0,0,0,0,0))
AutoN@reopen <- new("DevFac",FacID="D2",FacModel= FALSE,
meanList =c(0.02,0.015,0.01,0.005,0),volList =c(0.003, 0.002, 0.001, 0.001, 0))
AutoN@roDevFac <- new("DevFac",FacID="D3",FacModel= FALSE,
meanList =c(1.05,1.1,1,1,1),volList =c(0.00589,0.0037,0.00632,0.00815,0))
AutoN@reopenLag <- new("Exponential", p1 =0.01)
AutoN@resettleLag <- new("Exponential", p1 =0.25)
simobj <- new("Simulation", lines=lines, types=types, 
claimobjs= list(AutoN),workingFolder=tempdir())
simobj@simNo <- 1
simobj@iRBNER <-FALSE
simobj@iROPEN <-FALSE
simobj@iIBNR <-TRUE
simobj@iUPR <-FALSE
simdata <- claimSimulation(simobj,claimdata, startDate = as.Date("2012-01-01"), 
evaluationDate = as.Date("2016-12-31"), futureDate = as.Date("2017-12-31"))

An S4 class to represent a claim type.

Description

An S4 class to represent a claim type.

Slots

simno

The simulation index.

line

A string to identify the business line that the claim belongs to.

claimType

A string to identify the type of the claim. It further classifies the claims within a business line. For example, the type could be based on the size of the loss.

iRBNER

A Boolean variable to indicate whether RBNER (open claims) should be simulated.

iROPEN

A Boolean variable to indicate whether claim reopen should be simulated.

iIBNR

A Boolean variable to indicate whether IBNR claims should be simulated.

iUPR

A Boolean variable to indicate whether future claims should be simulated.

fIBNER

IBNER development factor.

severity

Severity distribution.

frequency

Frequency distribution.

reportLag

Report lag distribution.

settlementLag

Settlement lag distribution.

reopen

Claim reopen probability based on the number of years after settlement till valuation date.

reopenLag

Reopen lag distribution.

resettleLag

Resettlement lag distribution.

roDevFac

Reopened claim development factor.

ioDevFac

A numeric variable to indicate the method of loss development for open claim severity. 1: Conditional distribution based on paid loss; 2: conditional distribution based on incurred loss; 3: year-to-year development factors

irDevFac

A numeric variable to indicate the method of loss development for claim reopen severity simulation. 1: Conditional distribution based on paid loss; 2: conditional distribution based on incurred loss; 3: year-to-year development factors

freqIndex

Frequency distribution time index.

severityIndex

Severity distribution time index.

exposureIndex

Exposure time index for IBNR or UPR.

iCopula

Whether copula is used to model severity, report lag and settlement lag.

ssrCopula

Copula object used for severity, report lag and settlement lag.

sdata

Indicating whether only closed claims (CLOSED) or closed + open claims (ALL) will be used for severity fitting.

p0

An yearly table that controls the probability of invalid claim, excluding these valid claims less than deductible based on development year. It is based on the DevFac class.

Experience data plotting.

Description

Experience data plotting.

Usage

copulaDataPlot(object, ...)

## S4 method for signature 'CopulaObj'
copulaDataPlot(object)

Arguments

object

Copula Object
...

Additional parameters that may or may not be used

Examples

library(cascsim)
dist1<-new("Pareto",p1=20,p2=3)
dist2<-new("Normal",p1=5,p2=3,min=0,max=20,truncated=TRUE)
nom.cop <- new("CopulaObj", param=c(0.5),marginal=list(dist1=dist1,dist2=dist2),dimension=2)
setObservation(nom.cop)<-copulaSample(nom.cop,100)
copulaDataPlot(nom.cop)

Copula fitting

Description

Copula fitting

Usage

copulaFit(object, ...)

## S4 method for signature 'CopulaObj'
copulaFit(object)

Arguments

object

Copula Object
...

Additional parameters that may or may not be used

Examples

library(cascsim)
#Prepare pseudo observation data
library(copula)
dist1<-new("Pareto",p1=20,p2=3)
dist2<-new("Normal",p1=5,p2=3,min=0,max=20,truncated=TRUE)
dist3<-new("Lognormal",p1=2,p2=1,min=0,max=100,truncated=TRUE)
normal.cop <- normalCopula(c(0.6, 0.36, 0.6), dim=3, dispstr="un")
x <- rCopula(1000, normal.cop)
x[,1]<-Quantile(dist1,x[,1])
x[,2]<-Quantile(dist2,x[,2])
x[,3]<-Quantile(dist3,x[,3])
#Create Copula Object and Fit it to observation data without goodness of fit test
nom.cop <- new("CopulaObj", param=c(0.5,0.5,0.5),marginal=list(dist1=dist1,dist2=dist2,dist3=dist3),
dimension=3,observation=x,fittest=FALSE)
nom.cop <- copulaFit(nom.cop)
nom.cop@coutput
#Create Copula Object and Fit it to observation data with goodness of fit test
clayton.cop <- claytonCopula(c(3), dim=2)
x <- rCopula(1000, clayton.cop)
x[,1]<-Quantile(dist1,x[,1])
x[,2]<-Quantile(dist2,x[,2])
cla.cop <- new("CopulaObj", type="clayton",param=c(3),
marginal=list(dist1=dist1,dist2=dist2),dimension=2,observation=x,fittest=TRUE)
cla.cop <- copulaFit(cla.cop)
cla.cop@coutput

Visualization Copula fitting

Description

Visualization Copula fitting

Usage

copulaFitPlot(object, ...)

## S4 method for signature 'CopulaObj'
copulaFitPlot(object)

Arguments

object

Copula Object
...

Additional parameters that may or may not be used

Examples

library(cascsim)
#Prepare pseudo observation data
library(copula)
dist1<-new("Pareto",p1=20,p2=3)
dist2<-new("Normal",p1=5,p2=3,min=0,max=20,truncated=TRUE)
dist3<-new("Lognormal",p1=2,p2=1,min=0,max=100,truncated=TRUE)
normal.cop <- normalCopula(c(0.6, 0.36, 0.6), dim=3, dispstr="un")
x <- rCopula(1000, normal.cop)
x[,1]<-Quantile(dist1,x[,1])
x[,2]<-Quantile(dist2,x[,2])
x[,3]<-Quantile(dist3,x[,3])
#Create Copula Object and Fit it to observation data without goodness of fit test
nom.cop <- new("CopulaObj", param=c(0.5,0.5,0.5),marginal=list(dist1=dist1,dist2=dist2,dist3=dist3),
dimension=3,observation=x,fittest=FALSE)
nom.cop <- copulaFit(nom.cop)
copulaFitPlot(nom.cop)
#Create Copula Object and Fit it to observation data with goodness of fit test
clayton.cop <- claytonCopula(c(3), dim=2)
x <- rCopula(1000, clayton.cop)
x[,1]<-Quantile(dist1,x[,1])
x[,2]<-Quantile(dist2,x[,2])
cla.cop <- new("CopulaObj", type="clayton",param=c(3),marginal=list(dist1=dist1,dist2=dist2),
dimension=2,observation=x,fittest=TRUE)
cla.cop <- copulaFit(cla.cop)
copulaFitPlot(cla.cop)

An S4 class to represent a copula object to model the correlation.

Description

An S4 class to represent a copula object to model the correlation.

Slots

type

The type of the copula object.

para

A numeric vector that contains copula parameter(s).

marginal

A list of Distribution objects.

dispstr

The format of symmetric positive definite matrix used by elliptical copula (Normal Copula, t Copula). The default is "un" for unstructured. Other choices include "ex" for exchangeable, "ar1" for AR(1), and "toep" for Toeplitz (toeplitz).

df

The number of degrees of freedom used in t Copula.

observation

A matrix that contains the experience data for copula fitting.

fitmethod

The method of copula fitting. Default is "mpl":maximum pseudo-likelihood estimator. Others include "ml": maximum likelihood assuming it is the true distribution; "itau": inversion of Kendall’s tau estimator; "irho": inversion of Spearman’s rho estimator.

fittest

Whether to run goodness of fit test for copula fitting. Goodness of fit test could take a long time to finish.

fitsucc

Whether a copula fitting is successful.

coutput

Goodness of fit results.

info

A character string that contains additional information of the copula to identify line/type/frequency/time lag/severity.

Copula plotting. Only for 2 or 3 variables

Description

Copula plotting. Only for 2 or 3 variables

Usage

copulaPlot(object, ...)

## S4 method for signature 'CopulaObj'
copulaPlot(object)

Arguments

object

Copula Object
...

Additional parameters that may or may not be used

Examples

library(cascsim)
dist1<-new("Pareto",p1=20,p2=3)
dist2<-new("Normal",p1=5,p2=3,min=0,max=20,truncated=TRUE)
nom.cop <- new("CopulaObj", param=c(0.5),marginal=list(dist1=dist1,dist2=dist2),dimension=2)
copulaPlot(nom.cop)

Copula sampling. It will generate correlated variables or percentiles when marginal distributions are not specified.

Description

Copula sampling. It will generate correlated variables or percentiles when marginal distributions are not specified.

Usage

copulaSample(object, n, ...)

## S4 method for signature 'CopulaObj,numeric'
copulaSample(object, n)

Arguments

object

Copula Object
n

Number of samples
...

Additional parameters that may or may not be used

Examples

library(cascsim)
dist1<-new("Pareto",p1=20,p2=3)
dist2<-new("Normal",p1=5,p2=3,min=0,max=20,truncated=TRUE)
nom.cop <- new("CopulaObj", param=c(0.5),marginal=list(dist1=dist1,dist2=dist2),dimension=2)
copulaSample(nom.cop,100)

Density function.

Description

Density function.

Usage

Density(object, x, ...)

## S4 method for signature 'Normal'
Density(object, x, log = FALSE)

## S4 method for signature 'Beta'
Density(object, x, log = FALSE)

## S4 method for signature 'Exponential'
Density(object, x, log = FALSE)

## S4 method for signature 'Gamma'
Density(object, x, log = FALSE)

## S4 method for signature 'Geometric'
Density(object, x, log = FALSE)

## S4 method for signature 'Lognormal'
Density(object, x, log = FALSE)

## S4 method for signature 'NegativeBinomial'
Density(object, x, log = FALSE)

## S4 method for signature 'Pareto'
Density(object, x, log = FALSE)

## S4 method for signature 'Poisson'
Density(object, x, log = FALSE)

## S4 method for signature 'Uniform'
Density(object, x, log = FALSE)

## S4 method for signature 'Weibull'
Density(object, x, log = FALSE)

## S4 method for signature 'Empirical'
Density(object, x, log = FALSE)

Arguments

object

Distribution Object
x

Variable value
...

Additional function arguments
log

Boolean variable to indicate whether to return log of probability

Examples

xPareto <- new("Pareto",p1=20,p2=3)
Density(xPareto,50)

An S4 class to represent a loss development schedule.

Description

An S4 class to represent a loss development schedule.

Slots

FacID

A character string to identify the loss development schedule.

FacModel

A boolean to indicate whether the loss development schedule is described as a model (TRUE) or a list of value (FALSE).

fun

A character string that indicates the model format in link function. Currently identity(linear), inverse(reciprocal linear), log(exponential), and exponential(loglinear) link functions(models) are supported. It is only used when model == TRUE.

distType

A character string that indicates the distribution of development factors. Currently normal, lognormal, and gamma distributions are supported. It is only used when model == FALSE.

xname

A vector that includes the names of explanatory variables. They will have to be matched exactly to the claim data file. It is only used when model == TRUE.

paras

A vector that contains the parameters of the model. It is only used when model == TRUE.

meanList

A vector that contains the mean yearly development factor if distribution type is Normal. It is mu for Lognormal distribution and shape for Gamma distribution. It is only used when model == FALSE.

volList

A vector that contains the volatility of yearly development factor if distribution type is Normal. It is sigma for Lognormal distribution and scale for Gamma distribution. It is used for simulating IBNER factors. It is only used when model == FALSE.

An S4 class to represent a distribution, either parametric or non-parametric.

Description

An S4 class to represent a distribution, either parametric or non-parametric.

Slots

p1

A number for the value of the first parameter (default: 0.8).

p2

A number for the value of the second parameter (default: 1).

p3

A number for the value of the third parameter (default: 0).

empirical

A matrix that defines an empirical distribution with values and probabilities.

min

A number that defines the minimum value of the variable (default: 1e-8 considering it is used for frequency and severity modeling).

max

A number that defines the maximum value of the variable (default: 1e8).

fitsucc

Whether a distribution fitting is successful.

info

A character string that contains additional information of the distribution to identify line/type/frequency or severity.

Plot function.

Description

Plot function.

Usage

doPlot(object, ...)

## S4 method for signature 'Distribution'
doPlot(object)

Arguments

object

Object
...

Additional function arguments

Examples

xPareto <- new("Pareto",p1=20,p2=3)
doPlot(xPareto)

Sampling from the distribution.

Description

Sampling from the distribution.

Usage

doSample(object, n, ...)

## S4 method for signature 'Normal,numeric'
doSample(object, n)

## S4 method for signature 'Beta,numeric'
doSample(object, n)

## S4 method for signature 'Exponential,numeric'
doSample(object, n)

## S4 method for signature 'Gamma,numeric'
doSample(object, n)

## S4 method for signature 'Lognormal,numeric'
doSample(object, n)

## S4 method for signature 'Pareto,numeric'
doSample(object, n)

## S4 method for signature 'Poisson,numeric'
doSample(object, n)

## S4 method for signature 'NegativeBinomial,numeric'
doSample(object, n)

## S4 method for signature 'Geometric,numeric'
doSample(object, n)

## S4 method for signature 'Uniform,numeric'
doSample(object, n)

## S4 method for signature 'Weibull,numeric'
doSample(object, n)

## S4 method for signature 'Empirical,numeric'
doSample(object, n)

Arguments

object

A Distribution Object
n

Number of samples
...

Additional function arguments

Examples

xPareto <- new("Pareto",p1=20,p2=3)
doSample(xPareto,10000)

Density function of Truncated Beta Distribution

Description

Density function of Truncated Beta Distribution

Cumulative probability function of Truncated Beta Distribution

Quantile function of Truncated Beta Distribution max(0,min(claim,limit)-deductible)

Random generation of Truncated Beta Distribution max(0,min(claim,limit)-deductible)

Usage

dtbeta(x, shape1, shape2, ncp = 0, min = 0, max = 1)

ptbeta(q, shape1, shape2, ncp = 0, min = 0, max = 1)

qtbeta(p, shape1, shape2, ncp = 0, min = 0, max = 1)

rtbeta(n, shape1, shape2, ncp = 0, min = 0, max = 1)

Arguments

x

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
shape1

distribution parameter
shape2

distribution parameter
ncp

non-centrality parameter (Default: 0)
min

Left truncation deductible
max

Right truncation limit
q

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
p

Value of the probability
n

Number of samples

Examples

dtbeta(0.6,1,2)
ptbeta(0.5,1,2)
qtbeta(0.5,1,2)
rtbeta(100,1,2)

Density function of truncated empirical distribution

Description

Density function of truncated empirical distribution

Cumulative probability function of truncated empirical distribution

Quantile function of truncated empirical distribution max(0,min(claim,limit)-deductible)

Random generation of Truncated empirical distribution max(0,min(claim,limit)-deductible)

Usage

dtempirical(x, cdf, min = 0, max = 1e+09)

ptempirical(q, cdf, min = 0, max = 1e+05)

qtempirical(p, cdf, min = 0, max = 1e+05)

rtempirical(n, cdf, min = 0, max = 1e+05)

Arguments

x

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
cdf

empirical distribution (cdf for continuous distribution and pmf for discrete distribution)
min

Left truncation deductible
max

Right truncation limit
q

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
p

Value of the probability
n

Number of samples

Examples

#discrete distribution
dtempirical(3,matrix(c(0.1,0.2,0.3,0.05,0.05,0.2,0.1,1:6,10),7,2),3,100)
#continuous distribution
dtempirical(30,matrix(c(seq(0.01,1,0.01),qnorm(seq(0.01,1,0.01),30,20)),100,2),200,10000000)
#discrete distribution
ptempirical(c(3,5,10),matrix(c(0.1,0.2,0.3,0.05,0.05,0.2,0.1,1:6,10),7,2),3,100)
#continuous distribution
ptempirical(350,matrix(c(seq(0.01,1,0.01),cumprod(c(1,rep(1.1,99)))),100,2),200,10000000)
#discrete distribution
qtempirical(c(0.3,0.65,1),matrix(c(0.1,0.2,0.3,0.05,0.05,0.2,0.1,1:6,10),7,2),3,100)
#continuous distribution
qtempirical(c(0.3,0.65,0.8),matrix(c(seq(0.01,1,0.01),
cumprod(c(1,rep(1.1,99)))),100,2),200,10000000)
#discrete distribution
rtempirical(100,matrix(c(0.1,0.2,0.3,0.05,0.05,0.2,0.1,1:6,10),7,2),3,100)
#continuous distribution
rtempirical(100,matrix(c(seq(0.01,1,0.01),cumprod(c(1,rep(1.1,99)))),100,2),200,10000000)

Density function of Truncated Exponential Distribution

Description

Density function of Truncated Exponential Distribution

Cumulative probability function of Truncated Exponential Distribution

Quantile function of Truncated Exponential Distribution max(0,min(claim,limit)-deductible)

Random generation of Truncated Exponential Distribution max(0,min(claim,limit)-deductible)

Usage

dtexp(x, rate, min = 0, max = 1e+09)

ptexp(q, rate, min = 0, max = 1e+09)

qtexp(p, rate, min = 0, max = 1e+09)

rtexp(n, rate, min = 0, max = 1e+09)

Arguments

x

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
rate

Distribution parameter
min

Left truncation deductible
max

Right truncation limit
q

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
p

Value of the probability
n

Number of samples

Examples

dtexp(5,0.1)
ptexp(5,0.1)
qtexp(0.5,0.1)
rtexp(100,0.1)

Density function of Truncated Gamma Distribution

Description

Density function of Truncated Gamma Distribution

Cumulative probability function of Truncated Gamma Distribution

Quantile function of Truncated Gamma Distribution max(0,min(claim,limit)-deductible)

Random generation of Truncated Gamma Distribution max(0,min(claim,limit)-deductible)

Usage

dtgamma(x, shape, scale, min = 0, max = 1e+09)

ptgamma(q, shape, scale, min = 0, max = 1e+09)

qtgamma(p, shape, scale, min = 0, max = 1e+09)

rtgamma(n, shape, scale, min = 0, max = 1e+09)

Arguments

x

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
shape

Shape parameter
scale

Scale parameter
min

Left truncation deductible
max

Right truncation limit
q

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
p

Value of the probability
n

Number of samples

Examples

dtgamma(2,3,2)
ptgamma(2,3,2)
qtgamma(0.5,3,2)
rtgamma(100,3,2)

Density function of Truncated Geometric Distribution

Description

Density function of Truncated Geometric Distribution

Cumulative probability function of Truncated Geometric Distribution

Quantile function of Truncated Geometric Distribution max(0,min(claim,limit)-deductible)

Random generation of Truncated Geometric Distribution max(0,min(claim,limit)-deductible)

Usage

dtgeom(x, prob, min = 0, max = 1e+09)

ptgeom(q, prob, min = 0, max = 1e+09)

qtgeom(p, prob, min = 0, max = 1e+09)

rtgeom(n, prob, min = 0, max = 1e+09)

Arguments

x

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
prob

Distribution parameter
min

Left truncation deductible
max

Right truncation limit
q

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
p

Value of the probability
n

Number of samples

Examples

dtgeom(3,0.3)
ptgeom(3,0.3)
qtgeom(0.7,0.3)
rtgeom(100,0.3)

Density function of Truncated Lognormal Distribution

Description

Density function of Truncated Lognormal Distribution

Cumulative probability function of Truncated Lognormal Distribution

Quantile function of Truncated Lognormal Distribution max(0,min(claim,limit)-deductible)

Random generation of Truncated Lognormal Distribution max(0,min(claim,limit)-deductible)

Usage

dtlnorm(x, meanlog, sdlog, min = 0, max = 1e+09)

ptlnorm(q, meanlog, sdlog, min = 0, max = 1e+09)

qtlnorm(p, meanlog, sdlog, min = 0, max = 1e+09)

rtlnorm(n, meanlog, sdlog, min = 0, max = 1e+09)

Arguments

x

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
meanlog

Mean of the log of the distribution
sdlog

Standard deviation of the log of the distribution
min

Left truncation deductible
max

Right truncation limit
q

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
p

Value of the probability
n

Number of samples

Examples

dtlnorm(20,3,0.5)
ptlnorm(20,3,0.5)
qtlnorm(0.5,3,0.5)
rtlnorm(100,3,0.5)

Density function of Truncated Negative Binomial Distribution

Description

Density function of Truncated Negative Binomial Distribution

Cumulative probability function of Truncated Negative Binomial Distribution

Quantile function of Truncated Negative Binomial Distribution max(0,min(claim,limit)-deductible)

Random generation of Truncated Negative Binomial Distribution max(0,min(claim,limit)-deductible)

Usage

dtnbinom(x, size, prob, min = 0, max = 1e+09)

ptnbinom(q, size, prob, min = 0, max = 1e+09)

qtnbinom(p, size, prob, min = 0, max = 1e+09)

rtnbinom(n, size, prob, min = 0, max = 1e+09)

Arguments

x

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
size

Number of successful trials
prob

Probability of success in each trial
min

Left truncation deductible
max

Right truncation limit
q

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
p

Value of the probability
n

Number of samples

Examples

dtnbinom(230,100,0.3)
ptnbinom(230,100,0.3)
qtnbinom(0.5,100,0.3)
rtnbinom(500,100,0.3)

Density function of Truncated Normal Distribution

Description

Density function of Truncated Normal Distribution

Cumulative probability function of Truncated Normal Distribution

Quantile function of Truncated Normal Distribution max(0,min(claim,limit)-deductible)

Random generation of Truncated Normal Distribution max(0,min(claim,limit)-deductible)

Usage

dtnorm(x, mean, sd, min = 0, max = 1e+09)

ptnorm(q, mean, sd, min = 0, max = 1e+09)

qtnorm(p, mean, sd, min = 0, max = 1e+09)

rtnorm(n, mean, sd, min = 0, max = 1e+09)

Arguments

x

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
mean

Mean of the untruncated Normal distribution
sd

Standard deviation of the untruncated Normal distribution
min

Left truncation (like deductible)
max

Right truncation (like limit)
q

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
p

Value of the probability
n

Number of samples

Examples

dtnorm(0.5,1,2)
ptnorm(0.5,1,2)
qtnorm(0.5,1,2)
rtnorm(100,1,2)

Density function of Truncated Pareto Distribution

Description

Density function of Truncated Pareto Distribution

Cumulative probability function of Truncated Pareto Distribution

Quantile function of Truncated Pareto Distribution max(0,min(claim,limit)-deductible)

Random generation of Truncated Pareto Distribution max(0,min(claim,limit)-deductible)

Usage

dtpareto(x, xm, alpha, min = xm, max = 1e+09)

ptpareto(q, xm, alpha, min = xm, max = 1e+09)

qtpareto(p, xm, alpha, min = xm, max = 1e+09)

rtpareto(n, xm, alpha, min = xm, max = 1e+09)

Arguments

x

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
xm

Threshold value
alpha

Model parameter
min

Left truncation deductible
max

Right truncation limit
q

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
p

Value of the probability
n

Number of samples

Examples

dtpareto(500,1000,2)
ptpareto(500,1000,2)
qtpareto(0.5,1000,2)
rtpareto(100,1000,2)

Density function of Truncated Poisson Distribution

Description

Density function of Truncated Poisson Distribution

Cumulative probability function of Truncated Poisson Distribution

Quantile function of Truncated Poisson Distribution max(0,min(claim,limit)-deductible)

Random generation of Truncated Poisson Distribution max(0,min(claim,limit)-deductible)

Usage

dtpois(x, lambda, min = 0, max = 1e+09)

ptpois(q, lambda, min = 0, max = 1e+09)

qtpois(p, lambda, min = 0, max = 1e+09)

rtpois(n, lambda, min = 0, max = 1e+09)

Arguments

x

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
lambda

Distribution parameter
min

Left truncation deductible
max

Right truncation limit
q

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
p

Value of the probability
n

Number of samples

Examples

dtpois(3,5)
ptpois(3,5)
qtpois(0.6,5)
rtpois(100,5)

Density function of Truncated Weibull Distribution

Description

Density function of Truncated Weibull Distribution

Cumulative probability function of Truncated Weibull Distribution

Quantile function of Truncated Weibull Distribution max(0,min(claim,limit)-deductible)

Random generation of Truncated Weibull Distribution max(0,min(claim,limit)-deductible)

Usage

dtweibull(x, shape, scale, min = 0, max = 1e+09)

ptweibull(q, shape, scale, min = 0, max = 1e+09)

qtweibull(p, shape, scale, min = 0, max = 1e+09)

rtweibull(n, shape, scale, min = 0, max = 1e+09)

Arguments

x

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
shape

Shape parameter
scale

Scale parameter
min

Left truncation deductible
max

Right truncation limit
q

Value of the variable after deductible and limit max(0,min(claim,limit)-deductible)
p

Value of the probability
n

Number of samples

Examples

dtweibull(2.5,2,3)
ptweibull(2.5,2,3)
qtweibull(0.5,2,3)
rtweibull(100,2,3)

Get the expected P0 based on settlement/close year.

Description

Get the expected P0 based on settlement/close year.

Usage

expectZeros(closeYear, zeroProb)

Arguments

closeYear

Development years that claims are settled. It could be a number or a numeric vector.
zeroProb

A vector that contains the P(0) based on development year.

Examples

zeroprob<-c(0.02,0.01,0.005,0.005,0.003,0)
expectZeros(c(2,3,6,9,100,1,2,3,4),zeroprob)

An S4 class to represent distribution fitting.

Description

An S4 class to represent distribution fitting.

Slots

observation

Raw data input containing loss sizes for severity analysis and number of losses for frequency analysis.

fitdata

Processed data for distribution fitting. Frequency data may be provided as occurrence dates. The class will transform them into frequency data before distribution fitting.

trend

Index object for detrending the data.

startDate

Start date of claim data used for distribution fitting. The trend Index should also start from the same date (year-month).

endDate

End date of claim data used for distribution fitting.

trail

Trial Distribution object to start fitting.

fitted

Fitted Distribution object.

reportLag

Report lag distribution to adjust frequency data.

iLag

Whether to adjust the frequency data with report lag distribution.

method

Distribution fitting method. Maximum likelihood estimation (mle), moment matching estimation(mme) and quantile matching estimation(qme) are available.

probs

A vector containing the percentiles to be matched if qme is used for fitting.

ifreq

A boolean indicating whether it is frequency data or severity data.

idate

A boolean indicating whether frequency data is provided as occurrence dates (TRUE) or number of occurrences (FALSE).

datelist

A vector containing occurrence dates. It could be a data field in a claim file.

freq

A character string indicating the frequency: "Annual" or "Monthly".

iDL

A boolean indicating whether deductible and limit is considered in distribution fitting.

limit

A vector containing the limit for each claim.

deductible

A vector containing the deductible for each claim.

p0

A number that is the probability of having a zero-amount claim after deductible.

dof

Degree of freedom.

psd

A vector containing the standard deviation of parameter estimation. It is only available for mle.

aic

Akaike information criterion.

bic

Bayesian information criterion.

chisq

Chi-Squared Test Statistic.

pchisq

p-value of Chi-Squared Test.

kstest

K-S Test Statistic. Only used for continuous distribution.

pkstest

p-value of K-S Test. Only used for continuous distribution.

soutput

Distribution fitting summary.

Compare the raw data and fitted distribution on density, CDF, Q-Q plot and P-P plot

Description

Compare the raw data and fitted distribution on density, CDF, Q-Q plot and P-P plot

Usage

fitPlot(object, ...)

## S4 method for signature 'FitDist'
fitPlot(object, n = missing)

Arguments

object

FitDist Object
...

Additional function arguments
n

Number of samples, should not be used in current setting

Examples

library(cascsim)
data(claimdata)

#frequecy fitting example
findex <- new("Index", startDate = as.Date("2012-01-01"), tabulate=TRUE, monthlyIndex = c(rep(1,11),
cumprod(c(1,rep(1.5^(1/12),11))),cumprod(c(1.5,rep((1.3/1.5)^(1/12),11))),
cumprod(c(1.3,rep((1.35/1.3)^(1/12),11))),cumprod(c(1.35,rep((1.4/1.35)^(1/12),11))),1.4))
rawdata <- as.data.frame(as.Date(claimdata[(claimdata[,"LoB"]=="Auto" & 
claimdata[,"Type"]=="H"),]$occurrenceDate))
colnames(rawdata)<-"occurrenceDate"
xFit <- new("FitDist", observation=rawdata, trend=findex,startDate = as.Date("2012-01-01"),
method="mle",ifreq=TRUE,idate=TRUE, freq="Monthly")
xFit <- setFitdata(xFit)
setTrialDist(xFit) <- new("Poisson")
xFit@soutput
fitPlot(xFit)

Get the R copula object.

Description

Get the R copula object.

Usage

getCopula(object, ...)

## S4 method for signature 'CopulaObj'
getCopula(object)

Arguments

object

R copula object
...

Additional parameters that may or may not be used

Examples

library(cascsim)
dist1<-new("Pareto",p1=20,p2=3)
dist2<-new("Normal",p1=5,p2=3,min=0,max=20,truncated=TRUE)
nom.cop <- new("CopulaObj", param=c(0.5),marginal=list(dist1=dist1,dist2=dist2),dimension=2)
getCopula(nom.cop)

Retrieve index value based on dates.

Description

getIndex get a time index to reflect inflation, underwriting cycle or seasonality.

Usage

getIndex(object, ...)

## S4 method for signature 'Index'
getIndex(object, dates)

Arguments

object

Index Object
...

Additional function arguments
dates

dates to get index information

Examples

xindex <- new("Index", indexID = "IDX1", tabulate = FALSE, annualizedRate = 0.03)
xindex<-setIndex(xindex)
xindex@monthlyIndex
dates<-as.Date("2015-12-31")
getIndex(xindex,dates)

Get input data from an object.

Description

Get input data from an object.

Usage

getObservation(object, ...)

## S4 method for signature 'FitDist'
getObservation(object)

Arguments

object

Object
...

Additional function arguments

Examples

library(cascsim)
data(claimdata)

#frequecy fitting example
findex <- new("Index", startDate = as.Date("2012-01-01"), tabulate=TRUE, monthlyIndex = c(rep(1,11),
cumprod(c(1,rep(1.5^(1/12),11))),cumprod(c(1.5,rep((1.3/1.5)^(1/12),11))),
cumprod(c(1.3,rep((1.35/1.3)^(1/12),11))),cumprod(c(1.35,rep((1.4/1.35)^(1/12),11))),1.4))
rawdata <- as.data.frame(as.Date(claimdata[(claimdata[,"LoB"]=="Auto" & 
claimdata[,"Type"]=="H"),]$occurrenceDate))
colnames(rawdata)<-"occurrenceDate"
xFit <- new("FitDist", observation=rawdata, trend=findex,startDate = as.Date("2012-01-01"),
method="mle",ifreq=TRUE,idate=TRUE, freq="Monthly")
getObservation(xFit)

Get the trend index.

Description

Get the trend index.

Usage

getTrend(object, ...)

## S4 method for signature 'FitDist'
getTrend(object)

Arguments

object

Object
...

Additional function arguments

Examples

library(cascsim)
data(claimdata)

#frequecy fitting example
findex <- new("Index", startDate = as.Date("2012-01-01"), tabulate=TRUE, monthlyIndex = c(rep(1,11),
cumprod(c(1,rep(1.5^(1/12),11))),cumprod(c(1.5,rep((1.3/1.5)^(1/12),11))),
cumprod(c(1.3,rep((1.35/1.3)^(1/12),11))),cumprod(c(1.35,rep((1.4/1.35)^(1/12),11))),1.4))
rawdata <- as.data.frame(as.Date(claimdata[(claimdata[,"LoB"]=="Auto" & 
claimdata[,"Type"]=="H"),]$occurrenceDate))
colnames(rawdata)<-"occurrenceDate"
xFit <- new("FitDist", observation=rawdata, trend=findex,startDate = as.Date("2012-01-01"),
method="mle",ifreq=TRUE,idate=TRUE, freq="Monthly")
getTrend(xFit)

An S4 class to represent a time index for frequency or severity distribution.

Description

An S4 class to represent a time index for frequency or severity distribution.

Slots

indexID

A string to identify the index.

startDate

The date the index starts. It is expected to be consistent with the start date of the claim analysis.

tabulate

A boolean to indicate whether the index is determined by a constant rate (FALSE) or a series of index values (TRUE).

annualizedRate

A yearly index growth rate. It is only used when tabulate == FALSE.

yearlyIndex

A vector that contains index value on a yearly basis.

monthlyIndex

A vector that contains index value on a monthly basis.

seasonality

A vector that contains seasonal adjustment factor on a monthly basis.

K-S Test

Description

K-S Test

Usage

KSTest(object, ...)

## S4 method for signature 'FitDist'
KSTest(object, n = missing)

Arguments

object

FitDist Object
...

Additional function arguments
n

Number of samples, should not be used in current setting

Moment function of Pareto Distribution (PDF: alpha*xm^alpha/x^(alpha+1))

Description

Moment function of Pareto Distribution (PDF: alpha*xm^alpha/x^(alpha+1))

Density function of Pareto Distribution (PDF: alpha*xm^alpha/x^(alpha+1))

Cumulative probability function of Pareto Distribution (CDF: 1-(xm/x)^alpha)

Quantile function of Pareto Distribution

Random generation of Pareto Distribution

Usage

mpareto(order, xm, alpha = 3)

dpareto(x, xm, alpha = 3)

ppareto(q, xm, alpha = 3)

qpareto(p, xm, alpha = 3)

rpareto(n, xm, alpha = 3)

Arguments

order

Order of moment
xm

Threshold value
alpha

Default=3
x

Value of the variable
q

Value of the variable
p

Value of the probability
n

Number of samples

Examples

mpareto(1,1000,2)
dpareto(1500,1000,2)
ppareto(1500,1000,2)
qpareto(0.5,1000,2)
rpareto(100,1000,2)

Negative Loglikelihood.

Description

Negative Loglikelihood.

Usage

nloglik(paras, dist, fitdata, deductible, limit)

Arguments

paras

A vector contain distribution parameters.
dist

A Distribution Object.
fitdata

A vector of loss data for fitting.
deductible

A vector of deductible data for all loss data.
limit

A vector of limit data for all loss data.

Examples

paras<-c(1,1)
dist<-new("Normal")
fitdata<-rtnorm(1000,3,2,1,10)
deductible<-rep(1,1000)
limit<-rep(9,1000)
nloglik(paras,dist,fitdata,deductible,limit)
paras<-c(3,2)
nloglik(paras,dist,fitdata,deductible,limit)

Plotting the data for distribution fitting

Description

Plotting the data for distribution fitting

Usage

observationPlot(object, ...)

## S4 method for signature 'FitDist'
observationPlot(object)

Arguments

object

FitDist Object
...

Additional function arguments

Examples

library(cascsim)
data(claimdata)

#frequecy fitting example
findex <- new("Index", startDate = as.Date("2012-01-01"), tabulate=TRUE, monthlyIndex = c(rep(1,11),
cumprod(c(1,rep(1.5^(1/12),11))),cumprod(c(1.5,rep((1.3/1.5)^(1/12),11))),
cumprod(c(1.3,rep((1.35/1.3)^(1/12),11))),cumprod(c(1.35,rep((1.4/1.35)^(1/12),11))),1.4))
rawdata <- as.data.frame(as.Date(claimdata[(claimdata[,"LoB"]=="Auto" & 
claimdata[,"Type"]=="H"),]$occurrenceDate))
colnames(rawdata)<-"occurrenceDate"
xFit <- new("FitDist", observation=rawdata, trend=findex,startDate = as.Date("2012-01-01"),
method="mle",ifreq=TRUE,idate=TRUE, freq="Monthly")
xFit <- setFitdata(xFit)
setTrialDist(xFit) <- new("Poisson")
xFit@soutput
observationPlot(xFit)

Plotting the PDF of data and fitted distribution

Description

Plotting the PDF of data and fitted distribution

Usage

PDFPlot(object, ...)

## S4 method for signature 'FitDist'
PDFPlot(object, n = missing)

Arguments

object

FitDist Object
...

Additional function arguments
n

Number of samples, should not be used in current setting

Examples

library(cascsim)
data(claimdata)

#frequecy fitting example
findex <- new("Index", startDate = as.Date("2012-01-01"), tabulate=TRUE, monthlyIndex = c(rep(1,11),
cumprod(c(1,rep(1.5^(1/12),11))),cumprod(c(1.5,rep((1.3/1.5)^(1/12),11))),
cumprod(c(1.3,rep((1.35/1.3)^(1/12),11))),cumprod(c(1.35,rep((1.4/1.35)^(1/12),11))),1.4))
rawdata <- as.data.frame(as.Date(claimdata[(claimdata[,"LoB"]=="Auto" & 
claimdata[,"Type"]=="H"),]$occurrenceDate))
colnames(rawdata)<-"occurrenceDate"
xFit <- new("FitDist", observation=rawdata, trend=findex,startDate = as.Date("2012-01-01"),
method="mle",ifreq=TRUE,idate=TRUE, freq="Monthly")
xFit <- setFitdata(xFit)
setTrialDist(xFit) <- new("Poisson")
xFit@soutput
PDFPlot(xFit)

Cumulative probability function of empirical distribution using linear interpolation

Description

Cumulative probability function of empirical distribution using linear interpolation

Quantile function of Empirical Distribution

Random generation function of Empirical Distribution

Density function of Empirical Distribution based on simulation

Usage

pempirical(q, cdf)

qempirical(p, cdf)

rempirical(n, cdf)

dempirical(x, cdf)

Arguments

q

Value of the variable
cdf

empirical distribution (cdf for continuous distribution and pmf for discrete distribution)
p

Value of the probability
n

Number of samples
x

Value of the variable

Examples

#discrete distribution
pempirical(c(3,5,10),matrix(c(0.1,0.2,0.3,0.05,0.05,0.2,0.1,1:6,10),7,2))
#continuous distribution
pempirical(350,matrix(c(seq(0.01,1,0.01),cumprod(c(1,rep(1.1,99)))),100,2))
#discrete distribution
qempirical(c(0.3,0.65,1),matrix(c(0.1,0.2,0.3,0.05,0.05,0.2,0.1,1:6,10),7,2))
#continuous distribution
qempirical(c(0.3,0.65,0.8),matrix(c(seq(0.01,1,0.01),cumprod(c(1,rep(1.1,99)))),100,2))
#discrete distribution
rempirical(100,matrix(c(0.1,0.2,0.3,0.05,0.05,0.2,0.1,1:6,10),7,2))
#continuous distribution
rempirical(100,matrix(c(seq(0.01,1,0.01),cumprod(c(1,rep(1.1,99)))),100,2))
#discrete distribution
dempirical(3,matrix(c(0.1,0.2,0.3,0.05,0.05,0.2,0.1,1:6,10),7,2))
#continuous distribution
dempirical(30,matrix(c(seq(0.01,1,0.01),qnorm(seq(0.01,1,0.01),30,20)),100,2))

Plot text content

Description

Plot text content

Usage

plotText(content)

Arguments

content

A string to plot

Examples

plotText("You are awesome!")

P-P Plot of data and fitted distribution

Description

P-P Plot of data and fitted distribution

Usage

PPPlot(object, ...)

## S4 method for signature 'FitDist'
PPPlot(object, n = missing)

Arguments

object

FitDist Object
...

Additional function arguments
n

Number of samples, should not be used in current setting

Examples

library(cascsim)
data(claimdata)

#frequecy fitting example
findex <- new("Index", startDate = as.Date("2012-01-01"), tabulate=TRUE, monthlyIndex = c(rep(1,11),
cumprod(c(1,rep(1.5^(1/12),11))),cumprod(c(1.5,rep((1.3/1.5)^(1/12),11))),
cumprod(c(1.3,rep((1.35/1.3)^(1/12),11))),cumprod(c(1.35,rep((1.4/1.35)^(1/12),11))),1.4))
rawdata <- as.data.frame(as.Date(claimdata[(claimdata[,"LoB"]=="Auto" & 
claimdata[,"Type"]=="H"),]$occurrenceDate))
colnames(rawdata)<-"occurrenceDate"
xFit <- new("FitDist", observation=rawdata, trend=findex,startDate = as.Date("2012-01-01"),
method="mle",ifreq=TRUE,idate=TRUE, freq="Monthly")
xFit <- setFitdata(xFit)
setTrialDist(xFit) <- new("Poisson")
xFit@soutput
observationPlot(xFit)
PPPlot(xFit)

Probability function.

Description

Probability function.

Usage

Probability(object, q, ...)

## S4 method for signature 'Normal'
Probability(object, q)

## S4 method for signature 'Beta'
Probability(object, q)

## S4 method for signature 'Exponential'
Probability(object, q)

## S4 method for signature 'Gamma'
Probability(object, q)

## S4 method for signature 'Geometric'
Probability(object, q)

## S4 method for signature 'Lognormal'
Probability(object, q)

## S4 method for signature 'NegativeBinomial'
Probability(object, q)

## S4 method for signature 'Pareto'
Probability(object, q)

## S4 method for signature 'Poisson'
Probability(object, q)

## S4 method for signature 'Uniform'
Probability(object, q)

## S4 method for signature 'Weibull'
Probability(object, q)

## S4 method for signature 'Empirical'
Probability(object, q)

Arguments

object

Distribution Object
q

Variable value
...

Additional function arguments

Examples

xPareto <- new("Pareto",p1=20,p2=3)
Probability(xPareto,50)

Q-Q Plot of data and fitted distribution

Description

Q-Q Plot of data and fitted distribution

Usage

QQPlot(object, ...)

## S4 method for signature 'FitDist'
QQPlot(object, n = missing)

Arguments

object

FitDist Object
...

Additional function arguments
n

Number of samples, should not be used in current setting

Examples

library(cascsim)
data(claimdata)

#frequecy fitting example
findex <- new("Index", startDate = as.Date("2012-01-01"), tabulate=TRUE, monthlyIndex = c(rep(1,11),
cumprod(c(1,rep(1.5^(1/12),11))),cumprod(c(1.5,rep((1.3/1.5)^(1/12),11))),
cumprod(c(1.3,rep((1.35/1.3)^(1/12),11))),cumprod(c(1.35,rep((1.4/1.35)^(1/12),11))),1.4))
rawdata <- as.data.frame(as.Date(claimdata[(claimdata[,"LoB"]=="Auto" & 
claimdata[,"Type"]=="H"),]$occurrenceDate))
colnames(rawdata)<-"occurrenceDate"
xFit <- new("FitDist", observation=rawdata, trend=findex,startDate = as.Date("2012-01-01"),
method="mle",ifreq=TRUE,idate=TRUE, freq="Monthly")
xFit <- setFitdata(xFit)
setTrialDist(xFit) <- new("Poisson")
xFit@soutput
QQPlot(xFit)

Quantile function.

Description

Quantile function.

Usage

Quantile(object, p, ...)

## S4 method for signature 'Normal'
Quantile(object, p)

## S4 method for signature 'Beta'
Quantile(object, p)

## S4 method for signature 'Exponential'
Quantile(object, p)

## S4 method for signature 'Gamma'
Quantile(object, p)

## S4 method for signature 'Geometric'
Quantile(object, p)

## S4 method for signature 'Lognormal'
Quantile(object, p)

## S4 method for signature 'NegativeBinomial'
Quantile(object, p)

## S4 method for signature 'Pareto'
Quantile(object, p)

## S4 method for signature 'Poisson'
Quantile(object, p)

## S4 method for signature 'Uniform'
Quantile(object, p)

## S4 method for signature 'Weibull'
Quantile(object, p)

## S4 method for signature 'Empirical'
Quantile(object, p)

Arguments

object

Distribution Object
p

Probability
...

Additional function arguments

Examples

xPareto <- new("Pareto",p1=20,p2=3)
Quantile(xPareto,0.6)

Simulate whether closed claims will be reopened or not.

Description

Simulate whether closed claims will be reopened or not.

Usage

rreopen(closeYear, reopenProb)

Arguments

closeYear

Years after claim closure. It could be a number or a numeric vector.
reopenProb

A vector that contains the reopen probability based on closeYear.

Examples

reopenprob<-c(0.02,0.01,0.005,0.005,0.003,0)
rreopen(rep(2,1000),reopenprob)

Calculate the excess kurtosis of 10000 sampled values from the distribution.

Description

Calculate the excess kurtosis of 10000 sampled values from the distribution.

Usage

sampleKurtosis(object, ...)

## S4 method for signature 'Distribution'
sampleKurtosis(object)

Arguments

object

A Distribution Object
...

Additional function arguments

Examples

xLognormal <- new("Lognormal",p1=2,p2=3)
sampleKurtosis(xLognormal)

Calculate the mean of 100000 sampled values from the distribution.

Description

Calculate the mean of 100000 sampled values from the distribution.

Usage

sampleMean(object, ...)

## S4 method for signature 'Distribution'
sampleMean(object)

Arguments

object

A Distribution Object
...

Additional function arguments

Examples

xLognormal <- new("Lognormal",p1=2,p2=3)
sampleMean(xLognormal)

Calculate the standard deviation of 10000 sampled values from the distribution.

Description

Calculate the standard deviation of 10000 sampled values from the distribution.

Usage

sampleSd(object, ...)

## S4 method for signature 'Distribution'
sampleSd(object)

Arguments

object

A Distribution Object
...

Additional function arguments

Examples

xLognormal <- new("Lognormal",p1=2,p2=3)
sampleSd(xLognormal)

Calculate the skewness of 10000 sampled values from the distribution.

Description

Calculate the skewness of 10000 sampled values from the distribution.

Usage

sampleSkew(object, ...)

## S4 method for signature 'Distribution'
sampleSkew(object)

Arguments

object

A Distribution Object
...

Additional function arguments

Examples

xLognormal <- new("Lognormal",p1=2,p2=3)
sampleSkew(xLognormal)

Set the annualized level rate to construct the index. Only used when tabulate == FALSE.

Description

Set the annualized level rate to construct the index. Only used when tabulate == FALSE.

Usage

setAnnualizedRate(this, ...) <- value

## S4 replacement method for signature 'Index,numeric'
setAnnualizedRate(this) <- value

Arguments

this

Index Object
...

Additional function arguments
value

Numeric Value (default:0.02)

Examples

xindex <- new("Index")
setID(xindex)<-"IDX1"
setTabulate(xindex)<-FALSE
setAnnualizedRate(xindex)<-0.03
xindex<-setIndex(xindex)
xindex@monthlyIndex

Set copula parameters.

Description

Set copula parameters.

Usage

setCopulaParam(this, ...) <- value

## S4 replacement method for signature 'CopulaObj,numeric'
setCopulaParam(this) <- value

Arguments

this

Copula Object
...

Additional function arguments
value

The copula parameters

Examples

library(cascsim)
dist1<-new("Pareto",p1=20,p2=3)
dist2<-new("Normal",p1=5,p2=3,min=0,max=20,truncated=TRUE)
cop <- new("CopulaObj", param=c(0.5),marginal=list(dist1=dist1,dist2=dist2),dimension=2)
setCopulaParam(cop) <- 0.6

Set copula type.

Description

Set copula type.

Usage

setCopulaType(this, ...) <- value

## S4 replacement method for signature 'CopulaObj,character'
setCopulaType(this) <- value

Arguments

this

Copula Object
...

Additional function arguments
value

The copula type

Examples

library(cascsim)
dist1<-new("Pareto",p1=20,p2=3)
dist2<-new("Normal",p1=5,p2=3,min=0,max=20,truncated=TRUE)
cop <- new("CopulaObj", param=c(0.5),marginal=list(dist1=dist1,dist2=dist2),dimension=2)
setCopulaType(cop) <- "joe"

Set up an IBNER loss development schedule.

Description

setDevFac sets a loss development schedule, from either a predictive model or a year-to-year factor vector.

Usage

setDevFac(object, ...)

## S4 method for signature 'DevFac'
setDevFac(object)

Arguments

object

DevFac Object
...

Additional function arguments

Examples

xIBNERFactor <- new("DevFac", FacID = "IF1", FacModel = FALSE, meanList = c(1.26,1.1,1.05,1.02,1),
volList = rep(0.02,5))
xIBNERFactor<-setDevFac(xIBNERFactor)
xIBNERFactor

xIBNERFactor <- new("DevFac")
setID(xIBNERFactor)<-"IF1"
setFacModel(xIBNERFactor)<-TRUE
setFun(xIBNERFactor)<-"identity"
setXname(xIBNERFactor)<- c("x1","x2","x3")
setParas(xIBNERFactor)<-c(0.6,-0.2,0.01,-0.3,0.02,0.03,0.01,0.02)
xIBNERFactor<-setDevFac(xIBNERFactor)
xIBNERFactor

Set the degree of freedom for t Copula.

Description

Set the degree of freedom for t Copula.

Usage

setDf(this, ...) <- value

## S4 replacement method for signature 'CopulaObj,numeric'
setDf(this) <- value

Arguments

this

Copula Object
...

Additional function arguments
value

The degree of freedom. The default value is 3.

Examples

library(cascsim)
dist1<-new("Pareto",p1=20,p2=3)
dist2<-new("Normal",p1=5,p2=3,min=0,max=20,truncated=TRUE)
cop <- new("CopulaObj", type="t", param=c(0.5),marginal=list(dist1=dist1,dist2=dist2),dimension=2)
setDf(cop) <- 5

Set the dimension of the copula.

Description

Set the dimension of the copula.

Usage

setDimension(this, ...) <- value

## S4 replacement method for signature 'CopulaObj,numeric'
setDimension(this) <- value

Arguments

this

Copula Object
...

Additional function arguments
value

The dimension of the copula. It can also be set by providing marginal distributions

Examples

library(cascsim)
dist1<-new("Pareto",p1=20,p2=3)
dist2<-new("Normal",p1=5,p2=3,min=0,max=20,truncated=TRUE)
cop <- new("CopulaObj", param=c(0.5),marginal=list(dist1=dist1,dist2=dist2),dimension=2)
dist3<-new("Pareto",p1=10,p2=3)
setDimension(cop) <- 3
setMarginal(cop) <- list(dist1=dist1,dist2=dist2,dist3=dist3)

Set parameter matrix format of Elliptical copula.

Description

Set parameter matrix format of Elliptical copula.

Usage

setDispstr(this, ...) <- value

## S4 replacement method for signature 'CopulaObj,character'
setDispstr(this) <- value

Arguments

this

Copula Object
...

Additional function arguments
value

The matrix format. The default is "un" for unstructured. Other choices include "ex" for exchangeable, "ar1" for AR(1), and "toep" for Toeplitz (toeplitz).

Examples

library(cascsim)
dist1<-new("Pareto",p1=20,p2=3)
dist2<-new("Normal",p1=5,p2=3,min=0,max=20,truncated=TRUE)
cop <- new("CopulaObj", param=c(0.5),marginal=list(dist1=dist1,dist2=dist2),dimension=2)
setDispstr(cop) <- "ex"

Set the list of values and corresponding probabilities (Pr(X<value) for continuous variable and Pr(X==value) for discrete variable). It is only used for empirical distribution.

Description

Set the list of values and corresponding probabilities (Pr(X<value) for continuous variable and Pr(X==value) for discrete variable). It is only used for empirical distribution.

Usage

setEmpirical(this, ...) <- value

## S4 replacement method for signature 'Distribution,matrix'
setEmpirical(this) <- value

Arguments

this

Distribution Object
...

Additional function arguments.
value

Two-column matrix with values and probabilities dist <- new("Normal") setEmpirical(dist) <- matrix(c(0.01,0.25,0.5,0.75,0.99, 11,12,13,14,15), nrow = 5, ncol = 2) dist

Determine whether the development factor is determined by a predictive model or a fixed schedule by development year

Description

Determine whether the development factor is determined by a predictive model or a fixed schedule by development year

Usage

setFacModel(this, ...) <- value

## S4 replacement method for signature 'DevFac,logical'
setFacModel(this) <- value

Arguments

this

DevFac Object
...

Additional function arguments
value

Logical Value (default:FALSE)

Examples

xIBNERFactor <- new("DevFac")
setID(xIBNERFactor)<-"IF1"
setFacModel(xIBNERFactor)<-TRUE
setFun(xIBNERFactor)<-"identity"
setXname(xIBNERFactor)<- c("x1","x2","x3")
setParas(xIBNERFactor)<-c(0.6,-0.2,0.01,-0.3,0.02,0.03,0.01,0.02)
xIBNERFactor<-setDevFac(xIBNERFactor)
xIBNERFactor

Preparing the input data (observation) for distribution fitting, including detrending, translating occurrence dates to frequency data, etc.

Description

Preparing the input data (observation) for distribution fitting, including detrending, translating occurrence dates to frequency data, etc.

Usage

setFitdata(object, ...)

## S4 method for signature 'FitDist'
setFitdata(object)

Arguments

object

FitDist Object
...

Additional function arguments

Examples

library(cascsim)
data(claimdata)

#frequecy fitting example
findex <- new("Index", startDate = as.Date("2012-01-01"), tabulate=TRUE, monthlyIndex = c(rep(1,11),
cumprod(c(1,rep(1.5^(1/12),11))),cumprod(c(1.5,rep((1.3/1.5)^(1/12),11))),
cumprod(c(1.3,rep((1.35/1.3)^(1/12),11))),cumprod(c(1.35,rep((1.4/1.35)^(1/12),11))),1.4))
rawdata <- as.data.frame(as.Date(claimdata[(claimdata[,"LoB"]=="Auto" & 
claimdata[,"Type"]=="H"),]$occurrenceDate))
colnames(rawdata)<-"occurrenceDate"
xFit <- new("FitDist", observation=rawdata, trend=findex,startDate = as.Date("2012-01-01"),
method="mle",ifreq=TRUE,idate=TRUE, freq="Monthly")
xFit <- setFitdata(xFit)
xFit@fitdata

Set distribution fitting method.

Description

Set distribution fitting method.

Usage

setfitmethod(this, ...) <- value

## S4 replacement method for signature 'FitDist,character'
setfitmethod(this) <- value

Arguments

this

FitDist Object
...

Additional function arguments
value

A character string: "mle", "mme", or "qme"

Examples

library(cascsim)
data(claimdata)

#frequecy fitting example
findex <- new("Index", startDate = as.Date("2012-01-01"), tabulate=TRUE, monthlyIndex = c(rep(1,11),
cumprod(c(1,rep(1.5^(1/12),11))),cumprod(c(1.5,rep((1.3/1.5)^(1/12),11))),
cumprod(c(1.3,rep((1.35/1.3)^(1/12),11))),cumprod(c(1.35,rep((1.4/1.35)^(1/12),11))),1.4))
rawdata <- as.data.frame(as.Date(claimdata[(claimdata[,"LoB"]=="Auto" & 
claimdata[,"Type"]=="H"),]$occurrenceDate))
colnames(rawdata)<-"occurrenceDate"
xFit <- new("FitDist", observation=rawdata, trend=findex,startDate = as.Date("2012-01-01"),
method="mle",ifreq=TRUE,idate=TRUE, freq="Monthly")
setfitmethod(xFit) <- "mme"
xFit@method

Directly set the fitted distribution without fitting it to the data.

Description

Directly set the fitted distribution without fitting it to the data.

Usage

setFittedDist(this) <- value

## S4 replacement method for signature 'FitDist,Distribution'
setFittedDist(this) <- value

Arguments

this

FitDist Object
value

Fitted distribution

Examples

library(cascsim)
data(claimdata)

#frequecy fitting example
findex <- new("Index", startDate = as.Date("2012-01-01"), tabulate=TRUE, monthlyIndex = c(rep(1,11),
cumprod(c(1,rep(1.5^(1/12),11))),cumprod(c(1.5,rep((1.3/1.5)^(1/12),11))),
cumprod(c(1.3,rep((1.35/1.3)^(1/12),11))),cumprod(c(1.35,rep((1.4/1.35)^(1/12),11))),1.4))
rawdata <- as.data.frame(as.Date(claimdata[(claimdata[,"LoB"]=="Auto" & 
claimdata[,"Type"]=="H"),]$occurrenceDate))
colnames(rawdata)<-"occurrenceDate"
xFit <- new("FitDist", observation=rawdata, trend=findex,startDate = as.Date("2012-01-01"),
method="mle",ifreq=TRUE,idate=TRUE, freq="Monthly")
xFit <- setFitdata(xFit)
setTrialDist(xFit) <- new("Poisson")
xFit@fitted

Set the data frequency.

Description

Set the data frequency.

Usage

setfreq(this, ...) <- value

## S4 replacement method for signature 'FitDist,character'
setfreq(this) <- value

Arguments

this

FitDist Object
...

Additional function arguments
value

A character string: "Annual" or "Monthly"

Examples

library(cascsim)
data(claimdata)

#frequecy fitting example
findex <- new("Index", startDate = as.Date("2012-01-01"), tabulate=TRUE, monthlyIndex = c(rep(1,11),
cumprod(c(1,rep(1.5^(1/12),11))),cumprod(c(1.5,rep((1.3/1.5)^(1/12),11))),
cumprod(c(1.3,rep((1.35/1.3)^(1/12),11))),cumprod(c(1.35,rep((1.4/1.35)^(1/12),11))),1.4))
rawdata <- as.data.frame(as.Date(claimdata[(claimdata[,"LoB"]=="Auto" & 
claimdata[,"Type"]=="H"),]$occurrenceDate))
colnames(rawdata)<-"occurrenceDate"
xFit <- new("FitDist", observation=rawdata, trend=findex,startDate = as.Date("2012-01-01"),
method="mle",ifreq=TRUE,idate=TRUE, freq="Annual")
setfreq(xFit) <- "Monthly"
xFit@freq

Set the model format/link function (identity/inverse/log/exponential). Only used when FacModel == TRUE.

Description

Set the model format/link function (identity/inverse/log/exponential). Only used when FacModel == TRUE.

Usage

setFun(this, ...) <- value

## S4 replacement method for signature 'DevFac,character'
setFun(this) <- value

Arguments

this

DevFac Object
...

Additional function arguments
value

String Value (default:"identity")

Examples

xIBNERFactor <- new("DevFac")
setID(xIBNERFactor)<-"IF1"
setFacModel(xIBNERFactor)<-TRUE
setFun(xIBNERFactor)<-"identity"
setXname(xIBNERFactor)<- c("x1","x2","x3")
setParas(xIBNERFactor)<-c(0.6,-0.2,0.01,-0.3,0.02,0.03,0.01,0.02)
xIBNERFactor<-setDevFac(xIBNERFactor)
xIBNERFactor

setID Set the ID for an object

Description

setID Set the ID for an object

Usage

setID(this, ...) <- value

## S4 replacement method for signature 'Index,character'
setID(this) <- value

## S4 replacement method for signature 'DevFac,character'
setID(this) <- value

Arguments

this

Self
...

Additional function arguments
value

ID

Examples

xindex <- new("Index")
setID(xindex)<-"IDX1"
xindex@indexID

Set whether occurrence dates will be used for frequency data.

Description

Set whether occurrence dates will be used for frequency data.

Usage

setidate(this, ...) <- value

## S4 replacement method for signature 'FitDist,logical'
setidate(this) <- value

Arguments

this

FitDist Object
...

Additional function arguments
value

A boolean

Examples

library(cascsim)
data(claimdata)

#frequecy fitting example
findex <- new("Index", startDate = as.Date("2012-01-01"), tabulate=TRUE, monthlyIndex = c(rep(1,11),
cumprod(c(1,rep(1.5^(1/12),11))),cumprod(c(1.5,rep((1.3/1.5)^(1/12),11))),
cumprod(c(1.3,rep((1.35/1.3)^(1/12),11))),cumprod(c(1.35,rep((1.4/1.35)^(1/12),11))),1.4))
rawdata <- as.data.frame(as.Date(claimdata[(claimdata[,"LoB"]=="Auto" & 
claimdata[,"Type"]=="H"),]$occurrenceDate))
colnames(rawdata)<-"occurrenceDate"
xFit <- new("FitDist", observation=rawdata, trend=findex,startDate = as.Date("2012-01-01"),
method="mle",ifreq=TRUE,idate=FALSE, freq="Monthly")
setidate(xFit) <- TRUE
xFit@idate

Set the data type: frequency or severity/time lag.

Description

Set the data type: frequency or severity/time lag.

Usage

setifreq(this, ...) <- value

## S4 replacement method for signature 'FitDist,logical'
setifreq(this) <- value

Arguments

this

FitDist Object
...

Additional function arguments
value

A boolean

Examples

library(cascsim)
data(claimdata)

#frequecy fitting example
findex <- new("Index", startDate = as.Date("2012-01-01"), tabulate=TRUE, monthlyIndex = c(rep(1,11),
cumprod(c(1,rep(1.5^(1/12),11))),cumprod(c(1.5,rep((1.3/1.5)^(1/12),11))),
cumprod(c(1.3,rep((1.35/1.3)^(1/12),11))),cumprod(c(1.35,rep((1.4/1.35)^(1/12),11))),1.4))
rawdata <- as.data.frame(as.Date(claimdata[(claimdata[,"LoB"]=="Auto" & 
claimdata[,"Type"]=="H"),]$occurrenceDate))
colnames(rawdata)<-"occurrenceDate"
xFit <- new("FitDist", observation=rawdata, trend=findex,startDate = as.Date("2012-01-01"),
method="mle",ifreq=TRUE,idate=TRUE, freq="Monthly")
setifreq(xFit) <- FALSE
xFit@ifreq

Set up a time index for frequency or severity.

Description

setIndex sets a time index to reflect inflation, underwriting cycle or seasonality.

Usage

setIndex(object, ...)

## S4 method for signature 'Index'
setIndex(object)

Arguments

object

Index Object
...

Additional function arguments

Examples

xindex <- new("Index", indexID = "IDX1", tabulate = FALSE, annualizedRate = 0.03)
xindex<-setIndex(xindex)
xindex@monthlyIndex

xindex <- new("Index")
setID(xindex)<-"IDX1"
setTabulate(xindex)<-TRUE
setAnnualizedRate(xindex)<-0.03
setYearlyIndex(xindex)<- c(1,1.05,1.2,0.95,1.3)
set.seed(123)
setSeasonality(xindex)<-rnorm(12,mean=1,sd=0.03)
xindex<-setIndex(xindex)
xindex@monthlyIndex

Set the marginal distributions of the copula.

Description

Set the marginal distributions of the copula.

Usage

setMarginal(this, ...) <- value

## S4 replacement method for signature 'CopulaObj,list'
setMarginal(this) <- value

Arguments

this

Copula Object
...

Additional function arguments
value

The list of marginal distributions.

Examples

library(cascsim)
dist1<-new("Pareto",p1=20,p2=3)
dist2<-new("Normal",p1=5,p2=3,min=0,max=20,truncated=TRUE)
cop <- new("CopulaObj", param=c(0.5),marginal=list(dist1=dist1,dist2=dist2),dimension=2)
dist3<-new("Pareto",p1=10,p2=3)
dist4<-new("Normal",p1=2,p2=3,min=0,max=20,truncated=TRUE)
setMarginal(cop) <- list(dist1=dist3,dist2=dist4)

Set the year-to-year loss development factor.

Description

setMeanList<- sets expected year-to-year loss development factor. Years after It is only used when ibnerfModel == FALSE.

Usage

setMeanList(this, ...) <- value

## S4 replacement method for signature 'DevFac,vector'
setMeanList(this) <- value

Arguments

this

DevFac Object
...

Additional function arguments
value

Numeric Vector

Examples

xIBNERFactor <- new("DevFac")
setID(xIBNERFactor)<-"IF1"
setFacModel(xIBNERFactor)<-FALSE
setMeanList(xIBNERFactor)<-c(1.26,1.1,1.05,1.02,1)
setVolList(xIBNERFactor)<-rep(0.02,5)
xIBNERFactor

Set the minimum of the distribution. For example, the distribution of settlement lag for open claims

Description

Set the minimum of the distribution. For example, the distribution of settlement lag for open claims

Usage

setMin(object, ...)

## S4 method for signature 'Distribution'
setMin(object, minval)

Arguments

object

A Distribution Object
...

Additional function arguments.
minval

The minimum value.

Examples

xLognormal <- new("Lognormal",p1=2,p2=3)
xLognormal <- setMin(xLognormal,50)

Set monthly index values.

Description

setMonthlyIndex<- sets monthly index values.

Usage

setMonthlyIndex(this, ...) <- value

## S4 replacement method for signature 'Index,vector'
setMonthlyIndex(this) <- value

Arguments

this

Index Object
...

Additional function arguments
value

Numeric Vector

Examples

xindex <- new("Index")
setID(xindex)<-"IDX1"
setTabulate(xindex)<-TRUE
setMonthlyIndex(xindex)<- rep(1,360)
xindex<-setIndex(xindex)
xindex@monthlyIndex

Input the raw data.

Description

Input the raw data.

Usage

setObservation(this) <- value

## S4 replacement method for signature 'CopulaObj,matrix'
setObservation(this) <- value

## S4 replacement method for signature 'FitDist,matrix'
setObservation(this) <- value

Arguments

this

FitDist Object or Copula Object
value

A data frame or a matrix. For FitDist object, it could be a two-column data frame with the occurrence date and loss size/number of occurrence. Or a one-column data frame with loss size (ifreq == FALSE) or number of occurrence (ifreq == TRUE && idate == FALSE) or occurrence dates (ifreq == TRUE && idate == TRUE). For Copula object, it could be a matrix with each column contains the experience data of a variable.

Examples

library(cascsim)
dist1<-new("Pareto",p1=20,p2=3)
dist2<-new("Normal",p1=5,p2=3,min=0,max=20,truncated=TRUE)
nom.cop <- new("CopulaObj", param=c(0.5),marginal=list(dist1=dist1,dist2=dist2),dimension=2)
setObservation(nom.cop)<-copulaSample(nom.cop,100)
nom.cop@observation

Set distribution parameters.

Description

Set distribution parameters.

Usage

setParams(this, ...) <- value

## S4 replacement method for signature 'Distribution,numeric'
setParams(this) <- value

Arguments

this

Distribution Object
...

Additional function arguments.
value

Numeric vector containing parameters examples dist <- new("Normal") setParams(dist) <- c(2,3) dist

Set the values of model parameters.

Description

setParas<- sets model parameters. Their order must match the order of c("Intercept","DevelopmentYear","IncurredLoss","OSRatio",xname,"Volatility"). "Volatility" stands for the volatility of the error term in the model and used to simulate IBNER development factors. The parameter vector is only used when ibnerfModel == TRUE.

Usage

setParas(this, ...) <- value

## S4 replacement method for signature 'DevFac,vector'
setParas(this) <- value

Arguments

this

DevFac Object
...

Additional function arguments
value

Numeric Vector

Examples

xIBNERFactor <- new("DevFac")
setID(xIBNERFactor)<-"IF1"
setFacModel(xIBNERFactor)<-TRUE
setFun(xIBNERFactor)<-"identity"
setXname(xIBNERFactor)<- c("x1","x2","x3")
setParas(xIBNERFactor)<-c(0.6,-0.2,0.01,-0.3,0.02,0.03,0.01,0.02)
xIBNERFactor<-setDevFac(xIBNERFactor)
xIBNERFactor

Set the percentiles to be matched. Only used when qme is chosen for fitting method.

Description

Set the percentiles to be matched. Only used when qme is chosen for fitting method.

Usage

setprobs(this, ...) <- value

## S4 replacement method for signature 'FitDist,vector'
setprobs(this) <- value

Arguments

this

FitDist Object
...

Additional function arguments
value

A numeric vector with values between 0 and 1.

Examples

library(cascsim)
data(claimdata)

#frequecy fitting example
findex <- new("Index", startDate = as.Date("2012-01-01"), tabulate=TRUE, monthlyIndex = c(rep(1,11),
cumprod(c(1,rep(1.5^(1/12),11))),cumprod(c(1.5,rep((1.3/1.5)^(1/12),11))),
cumprod(c(1.3,rep((1.35/1.3)^(1/12),11))),cumprod(c(1.35,rep((1.4/1.35)^(1/12),11))),1.4))
rawdata <- as.data.frame(as.Date(claimdata[(claimdata[,"LoB"]=="Auto" & 
claimdata[,"Type"]=="H"),]$occurrenceDate))
colnames(rawdata)<-"occurrenceDate"
xFit <- new("FitDist", observation=rawdata, trend=findex,startDate = as.Date("2012-01-01"),
method="mle",ifreq=TRUE,idate=TRUE, freq="Monthly")
setprobs(xFit) <- c(0.1,0.5,0.9)
xFit@probs

Set the min and max of the variable.

Description

Set the min and max of the variable.

Usage

setRange(this, ...) <- value

## S4 replacement method for signature 'Distribution,numeric'
setRange(this) <- value

Arguments

this

Distribution Object
...

Additional function arguments.
value

a two-element vector contains min and max.

Set up the rectangle based on simulated data.

Description

setRectangle sets up the rectangle based on a data file.

Usage

setRectangle(object, data, ...)

## S4 method for signature 'Triangle,data.frame'
setRectangle(object, data,
  evaluationDate = as.Date("2016-12-31"),
  futureDate = as.Date("2017-12-31"), lob = "Total", ctype = "Total")

Arguments

object

Triangle Object
data

Simulated Data
...

Additional function arguments.
evaluationDate

Evaluation Date;
futureDate

End of projection date;
lob

Line of Business;
ctype

Claim Type.

Set seasonality on a monthly basis.

Description

setSeasonality<- sets monthly multiplier to reflect seasonal impact.

Usage

setSeasonality(this, ...) <- value

## S4 replacement method for signature 'Index,vector'
setSeasonality(this) <- value

Arguments

this

Index Object
...

Additional function arguments
value

Numeric Vector (default:rep(1,12))

Examples

xindex <- new("Index")
setID(xindex)<-"IDX1"
setTabulate(xindex)<-TRUE
setAnnualizedRate(xindex)<-0.03
setYearlyIndex(xindex)<- c(1,1.05,1.2,0.95,1.3)
set.seed(123)
setSeasonality(xindex)<-rnorm(12,mean=1,sd=0.03)
xindex<-setIndex(xindex)
xindex@monthlyIndex

Set the start date for the claim simulation exercise

Description

Set the start date for the claim simulation exercise

Usage

setStartDate(this, ...) <- value

## S4 replacement method for signature 'Index,Date'
setStartDate(this) <- value

Arguments

this

Self
...

Additional function arguments
value

Start Date

Determine whether the index values are constructed from a constant rate or provided directly

Description

Determine whether the index values are constructed from a constant rate or provided directly

Usage

setTabulate(this, ...) <- value

## S4 replacement method for signature 'Index,logical'
setTabulate(this) <- value

Arguments

this

Index Object
...

Additional function arguments
value

Logical Value (default:FALSE)

Examples

xindex <- new("Index")
setID(xindex)<-"IDX1"
setTabulate(xindex)<-FALSE
setAnnualizedRate(xindex)<-0.03
xindex<-setIndex(xindex)
xindex@monthlyIndex

Set the trend with an Index Object.

Description

Set the trend with an Index Object.

Usage

setTrend(this, ...) <- value

## S4 replacement method for signature 'FitDist,Index'
setTrend(this) <- value

Arguments

this

FitDist Object
...

Additional function arguments
value

An Index Object

Examples

library(cascsim)
data(claimdata)

#frequecy fitting example
findex <- new("Index", startDate = as.Date("2012-01-01"), tabulate=TRUE, monthlyIndex = c(rep(1,11),
cumprod(c(1,rep(1.5^(1/12),11))),cumprod(c(1.5,rep((1.3/1.5)^(1/12),11))),
cumprod(c(1.3,rep((1.35/1.3)^(1/12),11))),cumprod(c(1.35,rep((1.4/1.35)^(1/12),11))),1.4))
rawdata <- as.data.frame(as.Date(claimdata[(claimdata[,"LoB"]=="Auto" & 
claimdata[,"Type"]=="H"),]$occurrenceDate))
colnames(rawdata)<-"occurrenceDate"
xFit <- new("FitDist", observation=rawdata, startDate = as.Date("2012-01-01"),
method="mle",ifreq=TRUE,idate=TRUE, freq="Monthly")
setTrend(xFit) <- findex
xFit@trend

Distribution fitting and testing.

Description

Distribution fitting and testing.

Usage

setTrialDist(this) <- value

## S4 replacement method for signature 'FitDist,Distribution'
setTrialDist(this) <- value

Arguments

this

FitDist Object
value

Distribution to fit to

Examples

library(cascsim)
data(claimdata)

#frequecy fitting example
findex <- new("Index", startDate = as.Date("2012-01-01"), tabulate=TRUE, monthlyIndex = c(rep(1,11),
cumprod(c(1,rep(1.5^(1/12),11))),cumprod(c(1.5,rep((1.3/1.5)^(1/12),11))),
cumprod(c(1.3,rep((1.35/1.3)^(1/12),11))),cumprod(c(1.35,rep((1.4/1.35)^(1/12),11))),1.4))
rawdata <- as.data.frame(as.Date(claimdata[(claimdata[,"LoB"]=="Auto" & 
claimdata[,"Type"]=="H"),]$occurrenceDate))
colnames(rawdata)<-"occurrenceDate"
xFit <- new("FitDist", observation=rawdata, trend=findex,startDate = as.Date("2012-01-01"),
method="mle",ifreq=TRUE,idate=TRUE, freq="Monthly")
xFit <- setFitdata(xFit)
setTrialDist(xFit) <- new("Poisson")
xFit@soutput
observationPlot(xFit)
fitPlot(xFit)

Distribution fitting and testing. Same as setTrialDist except for error tolerance.

Description

Distribution fitting and testing. Same as setTrialDist except for error tolerance.

Usage

setTrialDistErr(this) <- value

## S4 replacement method for signature 'FitDist,Distribution'
setTrialDistErr(this) <- value

Arguments

this

FitDist Object
value

Distribution to fit to

Examples

library(cascsim)
data(claimdata)

#frequecy fitting example
findex <- new("Index", startDate = as.Date("2012-01-01"), tabulate=TRUE, monthlyIndex = c(rep(1,11),
cumprod(c(1,rep(1.5^(1/12),11))),cumprod(c(1.5,rep((1.3/1.5)^(1/12),11))),
cumprod(c(1.3,rep((1.35/1.3)^(1/12),11))),cumprod(c(1.35,rep((1.4/1.35)^(1/12),11))),1.4))
rawdata <- as.data.frame(as.Date(claimdata[(claimdata[,"LoB"]=="Auto" & 
claimdata[,"Type"]=="H"),]$occurrenceDate))
colnames(rawdata)<-"occurrenceDate"
xFit <- new("FitDist", observation=rawdata, trend=findex,startDate = as.Date("2012-01-01"),
method="mle",ifreq=TRUE,idate=TRUE, freq="Monthly")
xFit <- setFitdata(xFit)
setTrialDistErr(xFit) <- new("Poisson")
xFit@soutput
observationPlot(xFit)
fitPlot(xFit)

Set the indicator of truncated distribution.

Description

Set the indicator of truncated distribution.

Usage

setTruncated(this, ...) <- value

## S4 replacement method for signature 'Distribution,logical'
setTruncated(this) <- value

Arguments

this

Distribution Object
...

Additional function arguments.
value

Boolean to indicate whether the distribution is truncated by min and max or not.

Set up the upper triangle for non-simulated data.

Description

setUpperKeep sets up the upper triangle for non-simulated data.

Usage

setUpperKeep(object, data, ...)

## S4 method for signature 'Triangle,data.frame'
setUpperKeep(object, data,
  evaluationDate = as.Date("2016-12-31"), lob = "Total",
  ctype = "Total")

Arguments

object

Triangle Object
data

Claim Data
...

Additional function arguments.
evaluationDate

Evaluation Date;
lob

Line of Business;
ctype

Claim Type.

Examples

library(cascsim)
data(claimdata)
xTri <- new("Triangle", triID = "TRI1", type = "reportedCount", startDate=as.Date("2012-01-01"),
frequency="yearly", sim=1, percentile=50, iRBNER=TRUE, iROPEN=TRUE)
xTri<-setUpperTriangle(xTri,claimdata)
xTri<-setUpperKeep(xTri,claimdata)
xTri@upperkeep

xTri <- new("Triangle", triID = "TRI1", type = "closedCount", startDate=as.Date("2012-01-01"),
frequency="quarterly", sim=1, percentile=50, iRBNER=FALSE, iROPEN=TRUE)
xTri<-setUpperTriangle(xTri,claimdata)
xTri<-setUpperKeep(xTri,claimdata)
xTri@upperkeep

xTri <- new("Triangle", triID = "TRI1", type = "incurredLoss", startDate=as.Date("2012-01-01"),
frequency="yearly", sim=1, percentile=50, iRBNER=TRUE, iROPEN=FALSE)
xTri<-setUpperTriangle(xTri,claimdata)
xTri<-setUpperKeep(xTri,claimdata,lob="Auto",ctype="H")
xTri@upperkeep

Set up the upper triangle based on claim data.

Description

setUpperTriangle sets up the upper triangle based on a data file.

Usage

setUpperTriangle(object, data, ...)

## S4 method for signature 'Triangle,data.frame'
setUpperTriangle(object, data,
  evaluationDate = as.Date("2016-12-31"), lob = "Total",
  ctype = "Total")

Arguments

object

Triangle Object
data

Claim Data
...

Additional function arguments.
evaluationDate

Evaluation Date;
lob

Line of Business;
ctype

Claim Type.

Examples

library(cascsim)
data(claimdata)
xTri <- new("Triangle", triID = "TRI1", type = "reportedCount", startDate=as.Date("2012-01-01"),
frequency="yearly", sim=1, percentile=50)
xTri<-setUpperTriangle(xTri,claimdata)
xTri@upper

xTri <- new("Triangle", triID = "TRI1", type = "closedCount", startDate=as.Date("2012-01-01"),
frequency="quarterly", sim=1, percentile=50)
xTri<-setUpperTriangle(xTri,claimdata)
xTri@upper

xTri <- new("Triangle", triID = "TRI1", type = "incurredLoss", startDate=as.Date("2012-01-01"),
frequency="yearly", sim=1, percentile=50)
xTri<-setUpperTriangle(xTri,claimdata,lob="Auto",ctype="H")
xTri@upper

xTri <- new("Triangle", triID = "TRI1", type = "paidLoss", startDate=as.Date("2012-01-01"),
frequency="yearly", sim=1, percentile=50)
xTri<-setUpperTriangle(xTri,claimdata,lob="Auto",ctype="H")
xTri@upper

Set the year-to-year loss development factor volatility.

Description

setMeanList<- sets year-to-year loss development factor volatility. It is used to simulate loss development factor assuming a normal distribution. It can be set to zero for deterministic estimation. It is only used when ibnerfModel == FALSE.

Usage

setVolList(this, ...) <- value

## S4 replacement method for signature 'DevFac,vector'
setVolList(this) <- value

Arguments

this

DevFac Object
...

Additional function arguments
value

Numeric Vector

Examples

xIBNERFactor <- new("DevFac")
setID(xIBNERFactor)<-"IF1"
setFacModel(xIBNERFactor)<-FALSE
setMeanList(xIBNERFactor)<-c(1.26,1.1,1.05,1.02,1)
setVolList(xIBNERFactor)<-rep(0.02,5)
xIBNERFactor

Set additional explanatory variable names.

Description

setXname<- sets explanatory variable names in addition to "Intercept","DevelopmentYear","IncurredLoss", and "OSRatio". Additional variable names must match exactly with claim data. The xname vector is only used when ibnerfModel == TRUE.

Usage

setXname(this, ...) <- value

## S4 replacement method for signature 'DevFac,vector'
setXname(this) <- value

Arguments

this

DevFac Object
...

Additional function arguments
value

Character Vector

Examples

xIBNERFactor <- new("DevFac")
setID(xIBNERFactor)<-"IF1"
setFacModel(xIBNERFactor)<-TRUE
setFun(xIBNERFactor)<-"identity"
setXname(xIBNERFactor)<- c("x1","x2","x3")
setParas(xIBNERFactor)<-c(0.6,-0.2,0.01,-0.3,0.02,0.03,0.01,0.02)
xIBNERFactor<-setDevFac(xIBNERFactor)
xIBNERFactor

Set yearly index values.

Description

setYearlyIndex<- sets yearly index values. Monthly index will be constructed assuming constant growth rate during a year.

Usage

setYearlyIndex(this, ...) <- value

## S4 replacement method for signature 'Index,vector'
setYearlyIndex(this) <- value

Arguments

this

Index Object
...

Additional function arguments
value

Numeric Vector

Examples

xindex <- new("Index")
setID(xindex)<-"IDX1"
setTabulate(xindex)<-TRUE
setYearlyIndex(xindex)<- c(1,1.05,1.2,0.95,1.3)
xindex@yearlyIndex

Shift monthly index with a new start date and replace the unknown index value with zero.

Description

Shift monthly index with a new start date and replace the unknown index value with zero.

Usage

shiftIndex(object, ...)

## S4 method for signature 'Index'
shiftIndex(object, newStartDate, endDate)

Arguments

object

Index Object
...

Additional function arguments
newStartDate

new start date
endDate

end date

Examples

xindex <- new("Index", indexID = "IDX1", tabulate = FALSE, annualizedRate = 0.03)
xindex<-setIndex(xindex)
xindex@monthlyIndex
shiftIndex(xindex,as.Date("2016-10-15"),as.Date("2018-10-15"))
shiftIndex(xindex,as.Date("2010-10-15"),as.Date("2013-10-15"))

Simulate whether claims will have zero payment.

Description

Simulate whether claims will have zero payment.

Usage

simP0(devYear, zeroProb)

Arguments

devYear

Development Year. It could be a number or a numeric vector.
zeroProb

A vector that contains the probability of zero payment based on development year.

Examples

zeroprob<-c(0.02,0.01,0.005,0.005,0.003,0)
simP0(rep(2,1000),zeroprob)

Generate claim simulation result report in html

Description

Generate claim simulation result report in html

Usage

simReport(object, simSummary, ...)

## S4 method for signature 'Simulation,data.frame'
simReport(object, simSummary,
  simTriangle = NA, startDate = as.Date("2012-01-01"),
  evaluationDate = as.Date("2016-12-31"),
  futureDate = as.Date("2017-12-31"), iYear = FALSE)

Arguments

object

ClaimType object
simSummary

simulation result summary generated by simSummary
...

Additional parameters that may or may not be used.
simTriangle

triangle summary generated by simTriangle;
startDate

Date after which claims are analyzed;
evaluationDate

Date of evaluation for existing claims and IBNR;
futureDate

Date of evaluation for UPR (future claims);
iYear

Boolean that indicates whether summary by accident year should be produced in the report.

Examples

#run time is about 30s(>10s) and is commented out here to avoid long waiting time
#library(cascsim)
#data(claimdata)
#lines <- c("Auto")
#types <- c("N")
#AutoN <- new("ClaimType", line = "Auto", claimType = "N")
#AutoN@exposureIndex <- setIndex(new("Index",indexID="I1",tabulate= FALSE,
#startDate=as.Date("2012-01-01"), annualizedRate = 0)) # level exposure across time
#AutoN@frequency <- new("Poisson", p1 =50)
#AutoN@severityIndex <- setIndex(new("Index",indexID="I2",tabulate= FALSE,
#startDate=as.Date("2012-01-01"), annualizedRate = 0.02)) #assuming a 2% annual inflation
#AutoN@severity <- new("Lognormal", p1 =2, p2 =3)
#AutoN@deductible <- new("Empirical", empirical=matrix(c(0,1,100,100),2,2))
#AutoN@limit <- new("Empirical", empirical=matrix(c(0,1,1e8,1e8),2,2))
#AutoN@p0<-new("DevFac",meanList=c(0,0),volList=c(0,0))
#AutoN@reportLag <- new("Exponential", p1 =0.1)
#AutoN@settlementLag <- new("Exponential", p1 =0.05)
#AutoN@iCopula <- TRUE #use copula
#AutoN@ssrCopula <- new("CopulaObj", type ="normal", dimension = 3, 
#param = c(0.1,0.2,0.1))#A Gaussian Copula
#AutoN@ssrCopula@marginal <- c(AutoN@severity,AutoN@settlementLag,AutoN@reportLag)
#AutoN@laeDevFac <- new("DevFac",FacID="F1",FacModel= TRUE,fun="linear",
#paras =c(5,1.5,0.005,1.2,3))
#AutoN@fIBNER <- new("DevFac",FacID="D1",FacModel= FALSE,
#meanList =c(1.2,1.15,1.1,1.05,1),volList =c(0,0,0,0,0))
#AutoN@reopen <- new("DevFac",FacID="D2",FacModel= FALSE,
#meanList =c(0.02,0.015,0.01,0.005,0),volList =c(0.003, 0.002, 0.001, 0.001, 0))
#AutoN@roDevFac <- new("DevFac",FacID="D3",FacModel= FALSE,
#meanList =c(1.05,1.1,1,1,1),volList =c(0.00589,0.0037,0.00632,0.00815,0))
#AutoN@reopenLag <- new("Exponential", p1 =0.01)
#AutoN@resettleLag <- new("Exponential", p1 =0.25)
#simobj <- new("Simulation", lines=lines, types=types, 
#claimobjs= list(AutoN),workingFolder=tempdir())
#simobj@simNo <- 1
#simobj@iRBNER <-FALSE
#simobj@iROPEN <-FALSE
#simobj@iIBNR <-TRUE
#simobj@iUPR <-FALSE
#simdata <- claimSimulation(simobj,claimdata, startDate = as.Date("2012-01-01"), 
#evaluationDate = as.Date("2016-12-31"), futureDate = as.Date("2017-12-31"))
#simSummary <- simSummary(simobj,simdata, startDate = as.Date("2012-01-01"))
#simTriangle <- simTriangle(simobj,claimdata,simdata, startDate = as.Date("2016-01-01"))
#simReport(simobj, simSummary, simTriangle, startDate = as.Date("2012-01-01"))

Claim simulation result summary

Description

Claim simulation result summary

Usage

simSummary(object, simdata, ...)

## S4 method for signature 'Simulation,data.frame'
simSummary(object, simdata,
  startDate = as.Date("2012-01-01"),
  evaluationDate = as.Date("2016-12-31"),
  futureDate = as.Date("2017-12-31"))

Arguments

object

Simulation object
simdata

simulation data generated by claimSimulation
...

Additional parameters that may or may not be used.
startDate

Date after which claims are analyzed;
evaluationDate

Date of evaluation for existing claims and IBNR;
futureDate

Date of evaluation for UPR (future claims).

Examples

#run time is about 30s(>10s) and is commented out here to avoid long waiting time
#library(cascsim)
#data(claimdata)
#lines <- c("Auto")
#types <- c("N")
#AutoN <- new("ClaimType", line = "Auto", claimType = "N")
#AutoN@exposureIndex <- setIndex(new("Index",indexID="I1",tabulate= FALSE,
#startDate=as.Date("2012-01-01"), annualizedRate = 0)) # level exposure across time
#AutoN@frequency <- new("Poisson", p1 =50)
#AutoN@severityIndex <- setIndex(new("Index",indexID="I2",tabulate= FALSE,
#startDate=as.Date("2012-01-01"), annualizedRate = 0.02)) #assuming a 2% annual inflation
#AutoN@severity <- new("Lognormal", p1 =2, p2 =3)
#AutoN@deductible <- new("Empirical", empirical=matrix(c(0,1,100,100),2,2))
#AutoN@limit <- new("Empirical", empirical=matrix(c(0,1,1e8,1e8),2,2))
#AutoN@p0<-new("DevFac",meanList=c(0,0),volList=c(0,0))
#AutoN@reportLag <- new("Exponential", p1 =0.1)
#AutoN@settlementLag <- new("Exponential", p1 =0.05)
#AutoN@iCopula <- TRUE #use copula
#AutoN@ssrCopula <- new("CopulaObj", type ="normal", dimension = 3, 
#param = c(0.1,0.2,0.1))#A Gaussian Copula
#AutoN@ssrCopula@marginal <- c(AutoN@severity,AutoN@settlementLag,AutoN@reportLag)
#AutoN@laeDevFac <- new("DevFac",FacID="F1",FacModel= TRUE,fun="linear",
#paras =c(5,1.5,0.005,1.2,3))
#AutoN@fIBNER <- new("DevFac",FacID="D1",FacModel= FALSE,
#meanList =c(1.2,1.15,1.1,1.05,1),volList =c(0,0,0,0,0))
#AutoN@reopen <- new("DevFac",FacID="D2",FacModel= FALSE,
#meanList =c(0.02,0.015,0.01,0.005,0),volList =c(0.003, 0.002, 0.001, 0.001, 0))
#AutoN@roDevFac <- new("DevFac",FacID="D3",FacModel= FALSE,
#meanList =c(1.05,1.1,1,1,1),volList =c(0.00589,0.0037,0.00632,0.00815,0))
#AutoN@reopenLag <- new("Exponential", p1 =0.01)
#AutoN@resettleLag <- new("Exponential", p1 =0.25)
#simobj <- new("Simulation", lines=lines, types=types, 
#claimobjs= list(AutoN),workingFolder=tempdir())
#simobj@simNo <- 1
#simobj@iRBNER <-FALSE
#simobj@iROPEN <-FALSE
#simobj@iIBNR <-TRUE
#simobj@iUPR <-FALSE
#simdata <- claimSimulation(simobj,claimdata, startDate = as.Date("2012-01-01"), 
#evaluationDate = as.Date("2016-12-31"), futureDate = as.Date("2017-12-31"))
#simSummary <- simSummary(simobj,simdata, startDate = as.Date("2012-01-01"))

Claim simulation result triangles

Description

Claim simulation result triangles

Usage

simTriangle(object, claimdata, simdata, ...)

## S4 method for signature 'Simulation,data.frame,data.frame'
simTriangle(object, claimdata,
  simdata, frequency = "yearly", startDate = as.Date("2012-01-01"),
  evaluationDate = as.Date("2016-12-31"),
  futureDate = as.Date("2017-12-31"))

Arguments

object

Simulation object
claimdata

claim data used as basis for simulation
simdata

simulation data generated by claimSimulation
...

Additional parameters that may or may not be used.
frequency

triangle frequency, either "yearly" or "quarterly";
startDate

Date after which claims are analyzed;
evaluationDate

Date of evaluation for existing claims and IBNR;
futureDate

Date of evaluation for UPR (future claims).

Examples

#run time is about 30s(>10s) and is commented out here to avoid long waiting time
#library(cascsim)
#data(claimdata)
#lines <- c("Auto")
#types <- c("N")
#AutoN <- new("ClaimType", line = "Auto", claimType = "N")
#AutoN@exposureIndex <- setIndex(new("Index",indexID="I1",tabulate= FALSE,
#startDate=as.Date("2012-01-01"), annualizedRate = 0)) # level exposure across time
#AutoN@frequency <- new("Poisson", p1 =50)
#AutoN@severityIndex <- setIndex(new("Index",indexID="I2",tabulate= FALSE,
#startDate=as.Date("2012-01-01"), annualizedRate = 0.02)) #assuming a 2% annual inflation
#AutoN@severity <- new("Lognormal", p1 =2, p2 =3)
#AutoN@deductible <- new("Empirical", empirical=matrix(c(0,1,100,100),2,2))
#AutoN@limit <- new("Empirical", empirical=matrix(c(0,1,1e8,1e8),2,2))
#AutoN@p0<-new("DevFac",meanList=c(0,0),volList=c(0,0))
#AutoN@reportLag <- new("Exponential", p1 =0.1)
#AutoN@settlementLag <- new("Exponential", p1 =0.05)
#AutoN@iCopula <- TRUE #use copula
#AutoN@ssrCopula <- new("CopulaObj", type ="normal", dimension = 3, 
#param = c(0.1,0.2,0.1))#A Gaussian Copula
#AutoN@ssrCopula@marginal <- c(AutoN@severity,AutoN@settlementLag,AutoN@reportLag)
#AutoN@laeDevFac <- new("DevFac",FacID="F1",FacModel= TRUE,fun="linear",
#paras =c(5,1.5,0.005,1.2,3))
#AutoN@fIBNER <- new("DevFac",FacID="D1",FacModel= FALSE,
#meanList =c(1.2,1.15,1.1,1.05,1),volList =c(0,0,0,0,0))
#AutoN@reopen <- new("DevFac",FacID="D2",FacModel= FALSE,
#meanList =c(0.02,0.015,0.01,0.005,0),volList =c(0.003, 0.002, 0.001, 0.001, 0))
#AutoN@roDevFac <- new("DevFac",FacID="D3",FacModel= FALSE,
#meanList =c(1.05,1.1,1,1,1),volList =c(0.00589,0.0037,0.00632,0.00815,0))
#AutoN@reopenLag <- new("Exponential", p1 =0.01)
#AutoN@resettleLag <- new("Exponential", p1 =0.25)
#simobj <- new("Simulation", lines=lines, types=types, 
#claimobjs= list(AutoN),workingFolder=tempdir())
#simobj@simNo <- 1
#simobj@iRBNER <-FALSE
#simobj@iROPEN <-FALSE
#simobj@iIBNR <-TRUE
#simobj@iUPR <-FALSE
#simdata <- claimSimulation(simobj,claimdata, startDate = as.Date("2012-01-01"), 
#evaluationDate = as.Date("2016-12-31"), futureDate = as.Date("2017-12-31"))
#simSummary <- simSummary(simobj,simdata, startDate = as.Date("2012-01-01"))
#simTriangle <- simTriangle(simobj,claimdata,simdata, startDate = as.Date("2012-01-01"))

An S4 class to represent a simulation task.

Description

An S4 class to represent a simulation task.

Slots

startNo

The starting simulation index.

simNo

Number of simulation.

lines

A string vector to identify the business line(s) to be simulated.

types

A string vector to identify the claim types to be simulated.

iRBNER

A Boolean indicating whether IBNER claims need to be simulated.

iROPEN

A Boolean indicating whether claim reopening needs to be simulated.

iIBNR

A Boolean indicating whether IBNR claims need to be simulated.

iUPR

A Boolean indicating whether future claims need to be simulated.

claimobjs

A list of claim objects.

workingFolder

A string to specify the working folder where the simulation results will be saved.

iCopula

A Boolean indicating whether to use copula for frequency simulation.

freqCopula

Frequency copula.

iSummary

A Boolean indicating whether to summarzie the simulation results.

iReport

A Boolean indicating whether to generate an HTML report.

iFit

A Boolean indicating whether to fit some simulation parameters based on claim data.

ncores

Number of cores used for simulation.

tag

A unique tag for the simulation object including date and a random ID.

fitfile

A string to set the distribution fitting file name. If omitted, a name based on tag will be used.

copfile

A string to set the copula fitting file name. If omitted, a name based on tag will be used.

facfile

A string to set the factor fitting file name. Factor table is development year dependant. It could be the probability of zero payment, reopen probability, or loss development factors. If omitted, a name based on tag will be used.

fitRpt

A string to set the distribution fitting html report file name. If omitted, a name based on tag will be used.

simfile

A string to set the simulation result file name. If omitted, a name based on tag will be used.

sumfile

A string to set the summary file name. If omitted, a name based on tag will be used.

plog

A string to set the parallel run log file name. If omitted, a name based on tag will be used.

htmlRpt

A string to set the html report name. If omitted, a name based on tag will be used.

libpath

A string to the R liabrary folder where required packages are installed.

Calculate Theoretical Excessive Kurtosis of distribution. min and max are not applied

Description

Calculate Theoretical Excessive Kurtosis of distribution. min and max are not applied

Usage

TEKurt(object, ...)

## S4 method for signature 'Normal'
TEKurt(object)

## S4 method for signature 'Beta'
TEKurt(object)

## S4 method for signature 'Exponential'
TEKurt(object)

## S4 method for signature 'Gamma'
TEKurt(object)

## S4 method for signature 'Geometric'
TEKurt(object)

## S4 method for signature 'Lognormal'
TEKurt(object)

## S4 method for signature 'NegativeBinomial'
TEKurt(object)

## S4 method for signature 'Pareto'
TEKurt(object)

## S4 method for signature 'Poisson'
TEKurt(object)

## S4 method for signature 'Uniform'
TEKurt(object)

## S4 method for signature 'Weibull'
TEKurt(object)

Arguments

object

Distribution Object
...

Additional function arguments

Examples

xPareto <- new("Pareto",p1=20,p2=5)
TEKurt(xPareto)

Calculate Theoretical Mean of distribution. min and max are not applied

Description

Calculate Theoretical Mean of distribution. min and max are not applied

Usage

TMean(object, ...)

## S4 method for signature 'Normal'
TMean(object)

## S4 method for signature 'Beta'
TMean(object)

## S4 method for signature 'Exponential'
TMean(object)

## S4 method for signature 'Gamma'
TMean(object)

## S4 method for signature 'Geometric'
TMean(object)

## S4 method for signature 'Lognormal'
TMean(object)

## S4 method for signature 'NegativeBinomial'
TMean(object)

## S4 method for signature 'Pareto'
TMean(object)

## S4 method for signature 'Poisson'
TMean(object)

## S4 method for signature 'Uniform'
TMean(object)

## S4 method for signature 'Weibull'
TMean(object)

Arguments

object

Distribution Object
...

Additional function arguments

Examples

xPareto <- new("Pareto",p1=20,p2=3)
TMean(xPareto)

Convert US date mm/dd/yyyy to yyyy-mm-dd format

Description

Convert US date mm/dd/yyyy to yyyy-mm-dd format

Usage

toDate(d)

Arguments

d

vector of dates in possible US format

Examples

toDate("3/5/2017")

An S4 class to represent a triangle or rectangle object.

Description

An S4 class to represent a triangle or rectangle object.

Slots

triID

A character string to identify the triangle object.

type

A character string that indicates the triangle type, such as reportedCount, closedCount, paidLoss, and incurredLoss.

startDate

The start date for the accident year or Quarter.

frequency

A character that indicates the frequency of the triangle, "yearly" or "quarterly".

sim

A number that indicates the simulation number used to complete the rectangle. Zero means using the average value.

percentile

A number that indicates the percentile used to complete the rectangle. It is only used when sim is NA.

iRBNER

A Boolean that indicates whether open claims are simulated. If not, current information will be used for constructing rectangles. Otherwise, simulated data will be used.

iROPEN

A Boolean that indicates whether claim reopen are simulated. If not, current information will be used for constructing rectangles. Otherwise, simulated data will be used.

percentile

A number that indicates the percentile used to complete the rectangle. It is only used when sim is NA.

upper

A matrix that contains the upper triangle based on claim data.

upperkeep

A matrix that contains the upper triangle that are not simulated. It will be used to construct the rectangle for the non-simulated part.

rectangle

A matrix that contains the entire rectangle based on simulation data.

Truncate a numeric vector

Description

Truncate a numeric vector

Usage

truncate(x, lower, upper)

Arguments

x

A numeric vector
lower

Lower bound
upper

Upper bound

Examples

trunc(rnorm(100,3,6),0,7)

Calculate Theoretical Standard Deviation of distribution. min and max are not applied

Description

Calculate Theoretical Standard Deviation of distribution. min and max are not applied

Usage

TSD(object, ...)

## S4 method for signature 'Normal'
TSD(object)

## S4 method for signature 'Beta'
TSD(object)

## S4 method for signature 'Exponential'
TSD(object)

## S4 method for signature 'Gamma'
TSD(object)

## S4 method for signature 'Geometric'
TSD(object)

## S4 method for signature 'Lognormal'
TSD(object)

## S4 method for signature 'NegativeBinomial'
TSD(object)

## S4 method for signature 'Pareto'
TSD(object)

## S4 method for signature 'Poisson'
TSD(object)

## S4 method for signature 'Uniform'
TSD(object)

## S4 method for signature 'Weibull'
TSD(object)

Arguments

object

Distribution Object
...

Additional function arguments

Examples

xPareto <- new("Pareto",p1=20,p2=3)
TSD(xPareto)

Calculate Theoretical Skewness of distribution. min and max are not applied

Description

Calculate Theoretical Skewness of distribution. min and max are not applied

Usage

TSkewness(object, ...)

## S4 method for signature 'Normal'
TSkewness(object)

## S4 method for signature 'Beta'
TSkewness(object)

## S4 method for signature 'Exponential'
TSkewness(object)

## S4 method for signature 'Gamma'
TSkewness(object)

## S4 method for signature 'Geometric'
TSkewness(object)

## S4 method for signature 'Lognormal'
TSkewness(object)

## S4 method for signature 'NegativeBinomial'
TSkewness(object)

## S4 method for signature 'Pareto'
TSkewness(object)

## S4 method for signature 'Poisson'
TSkewness(object)

## S4 method for signature 'Uniform'
TSkewness(object)

## S4 method for signature 'Weibull'
TSkewness(object)

Arguments

object

Distribution Object
...

Additional function arguments

Examples

xPareto <- new("Pareto",p1=20,p2=4)
TSkewness(xPareto)

Calculate ultimate development factor based on current development year, a mean development factor schedule and its volatility. It is used to simulate the ultimate loss for open claims.

Description

Calculate ultimate development factor based on current development year, a mean development factor schedule and its volatility. It is used to simulate the ultimate loss for open claims.

Usage

ultiDevFac(Years, meanDevFac, sdDevFac = rep(0, length(meanDevFac)),
  distType = "normal")

Arguments

Years

Include two columns: Current development year and Settlement Year
meanDevFac

A vector that contains the expected development factor schedule for Normal distribution. It is mu for Lognormal distribution and shape for Gamma distribution.
sdDevFac

A vector that contains the standard deviation of expected development factor schedule for Normal distribution. It is sigma for Lognormal distribution and scale for Gamma distribution.
distType

distribution type for development factor. It can be "normal", "lognormal" or "gamma".

Examples

meanfac<-c(1.1,1.08,1.05,1.03,1.01,1)
volfac<-rep(0.02,6)
years<-matrix(c(1:6),3,2)
ultiDevFac(years,meanfac,volfac)