R: Extracting information about zero-claims and severity...
extract.prior
R Documentation
Extracting information about zero-claims and severity inflation
Description
A way of extracting information about zero-claims and severity development inflation through the DCL method applied to two counts triangles: number of payments and number of reported claims.
Usage
extract.prior(Xtriangle, Npaid, Ntriangle, Plots = TRUE , n.cal = NA ,
Fj.X = NA , Fj.N = NA , Fj.Npaid = NA )
Arguments
Xtriangle
The paid run-off triangle: incremental aggregated payments. It should be a matrix with incremental aggregated payments located in the upper triangle and the lower triangle consisting in missing or zero values.
Npaid
A run-off (incremental) triangle with the number of payments. It should be a matrix with the observed counts located in the upper triangle and the lower triangle consisting in missing or zero values. It should has the same dimension as Xtriangle (both in the same aggregation level (quarters, years,etc.))
Ntriangle
The counts data triangle: incremental number of reported claims. It should be a matrix with the observed counts located in the upper triangle and the lower triangle consisting in missing or zero values. It should has the same dimension as Xtriangle (both in the same aggregation level (quarters, years,etc.))
Plots
Logical. If TRUE (default) it is showed a two by one plot showing the extracted severity inflation in the development direction and the probability of zero-claims for each underwriting period.
n.cal
Integer specifying the number of most recent calendars which will be used to calculate the development factors. By default n.cal=NA and all the observed calendars are used (classical chain ladder).
Fj.X
Optional vector with lentgth m-1 (m being the dimension of the triangles) with the development factors to calculate the chain ladder estimates from Xtriangle. See more details in clm.
Fj.Npaid
Optional vector with lentgth m-1 with the development factors to calculate the chain ladder estimates from Npaid.
Fj.N
Optional vector with lentgth m-1 with the development factors to calculate the chain ladder estimates from Ntriangle.
Details
The function implements the strategy proposed in the paper by Martinez-Miranda, Nielsen, Verrall and Wuthrich (2013) to extract information for additional triangles (see "Section 5: An example showing how other data can be used to provide prior information in practice"). The derived severity inflation inflat.j does not extend to the tail. If you want provide the tail, by using dcl.predict.prior, the vector should be extended to have dimension 2m-1, otherwise the tail will be not provided (as was done in the cited paper).
Value
inflat.j
A vector with dimension m with the extracted severity inflation in the development direction.
Qi
A vector with dimension m with the extracted probability of zero-claims for undewriting period.
Author(s)
M.D. Martinez-Miranda, J.P. Nielsen and R. Verrall
References
Martinez-Miranda, M.D., Nielsen, J.P., Verrall, R. and Wuthrich, M.V. (2013) Double Chain Ladder, Claims Development Inflation and Zero Claims. Scandinavian Actuarial Journal. In press.
See Also
dcl.predict.prior, dcl.estimation
Examples
## Data application in Martinez-Miranda, Nielsen, Verrall and Wuthrich (2013)
data(NtrianglePrior)
data(NpaidPrior)
data(XtrianglePrior)
extract.prior(XtrianglePrior,NpaidPrior,NtrianglePrior)
Results
R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> library(DCL)
Loading required package: lattice
Loading required package: latticeExtra
Loading required package: RColorBrewer
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/DCL/extract.prior.Rd_%03d_medium.png", width=480, height=480)
> ### Name: extract.prior
> ### Title: Extracting information about zero-claims and severity inflation
> ### Aliases: extract.prior
> ### Keywords: Statistics
>
> ### ** Examples
>
> ## Data application in Martinez-Miranda, Nielsen, Verrall and Wuthrich (2013)
> data(NtrianglePrior)
> data(NpaidPrior)
> data(XtrianglePrior)
>
> extract.prior(XtrianglePrior,NpaidPrior,NtrianglePrior)
$inflat.j
[1] 0.7511558 1.1003897 2.8325640 7.0809882 12.5005313 14.4743474
[7] 12.8651793 17.3488108 26.1926812 24.3905249 23.6600806 40.2843130
[13] 2.0952557 NA
$Qi
[1] 0.2070538 0.2198485 0.2360260 0.2276527 0.2335186 0.2479112 0.2804041
[8] 0.3059233 0.3265810 0.3468118 0.3518048 0.3388062 0.3202681 0.3461808
>
>
>
>
>
>
> dev.off()
null device
1
>