Number of reported claims (adding prior knowledge example)

Description

It is a yearly run-off (incremental) triangle consisting of the number of reported claims during 14 years. These data were used in the empirical illustration provided by Martinez-Miranda, Nielsen, Verrall and Wuthrich (2013).

Usage

data(NtrianglePrior)

Format

Matrix with dimension 14 by 14: 14 undewriting years and 14 development years.

Source

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.

Examples

data(NtrianglePrior)

Plot.triangle(NtrianglePrior, Histogram=TRUE)
Plot.triangle(NtrianglePrior)

# Classical chain ladder method
clm(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/NtrianglePrior.Rd_%03d_medium.png", width=480, height=480)
> ### Name: NtrianglePrior
> ### Title: Number of reported claims (adding prior knowledge example)
> ### Aliases: NtrianglePrior
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(NtrianglePrior)
> 
> Plot.triangle(NtrianglePrior, Histogram=TRUE)
> Plot.triangle(NtrianglePrior)
> 
> # Classical chain ladder method
> clm(NtrianglePrior)
$triangle.hat
            V1       V2        V3       V4       V5       V6        V7
 [1,] 18757.51 2581.481 112.31863 23.84187 7.732717 3.585261 1.8251017
 [2,] 17280.79 2378.249 103.47613 21.96487 7.123943 3.303004 1.6814170
 [3,] 16544.17 2276.873  99.06533 21.02859 6.820276 3.162209 1.6097445
 [4,] 14677.32 2019.950  87.88677 18.65572 6.050674 2.805385 1.4281005
 [5,] 14314.44 1970.008  85.71384 18.19447 5.901076 2.736024 1.3927918
 [6,] 14178.74 1951.333  84.90129 18.02199 5.845135 2.710087 1.3795884
 [7,] 13913.42 1914.819  83.31258 17.68475 5.735759 2.659374 1.3537730
 [8,] 13663.78 1880.462  81.81775 17.36745 5.632845 2.611659 1.3294830
 [9,] 12697.66 1747.502  76.03272 16.13946 5.234568 2.426998 1.2354802
[10,] 11941.90 1643.491  71.50726 15.17884 4.923007 2.282543 1.1619445
[11,] 10953.09 1507.406  65.58631 13.92200 4.515371 2.093544 1.0657331
[12,] 10250.86 1410.763  61.38140 13.02943 4.225880 1.959322 0.9974063
[13,] 10119.34 1392.663  60.59388 12.86226 4.171661 1.934184 0.9846095
[14,] 10435.00 1436.105  62.48405 13.26348 4.301792 1.994518 1.0153234
             V8        V9       V10       V11 V12 V13 V14
 [1,] 1.3683324 1.3712636 0.6898322 0.2788815   0   0   0
 [2,] 1.2606077 1.2633082 0.6355238 0.2569260   0   0   0
 [3,] 1.2068727 1.2094581 0.6084338 0.2459742   0   0   0
 [4,] 1.0706889 1.0729825 0.5397779 0.2182184   0   0   0
 [5,] 1.0442169 1.0464539 0.5264324 0.2128231   0   0   0
 [6,] 1.0343180 1.0365337 0.5214419 0.2108056   0   0   0
 [7,] 1.0149634 1.0171376 0.5116844 0.2068609   0   0   0
 [8,] 0.9967524 0.9988877 0.5025036 0.2031493   0   0   0
 [9,] 0.9262758 0.9282601 0.4669734 0.1887854   0   0   0
[10,] 0.8711439 0.8730101 0.4391792 0.1775489   0   0   0
[11,] 0.7990114 0.8007230 0.4028142 0.1628475   0   0   0
[12,] 0.7477848 0.7493867 0.3769888 0.1524069   0   0   0
[13,] 0.7381907 0.7397720 0.3721520 0.1504515   0   0   0
[14,] 0.7612178 0.7628485 0.3837609 0.1551447   0   0   0

$alpha
 [1] 21492.00 19800.00 18956.00 16817.00 16401.21 16245.73 15941.74 15655.70
 [9] 14548.75 13682.81 12549.84 11745.24 11594.55 11956.23

$beta
 [1] 8.727669e-01 1.201136e-01 5.226067e-03 1.109337e-03 3.597951e-04
 [6] 1.668184e-04 8.492005e-05 6.366706e-05 6.380344e-05 3.209716e-05
[11] 1.297606e-05 0.000000e+00 0.000000e+00 0.000000e+00

$Fj
      V2       V3       V4       V5       V6       V7       V8       V9 
1.137624 1.005264 1.001111 1.000360 1.000167 1.000085 1.000064 1.000064 
     V10      V11      V12      V13      V14 
1.000032 1.000013 1.000000 1.000000 1.000000 

> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>