Paid data (BDCL example)

Description

Real motor data from a major insurer. It is a run-off (incremental) triangle consisting of the aggregated payments during 19 years. These data were used in the empirical illustration provided by Martinez-Miranda, Nielsen and Verrall (2013).

Usage

data(XtriangleBDCL)

Format

Matrix with dimension 19 by 19: 19 undewriting years and 19 development years.

References

Martinez-Miranda, M.D., Nielsen, J.P. and Verrall, R. (2013) Double Chain Ladder and Bornhuetter-Fergusson. North American Actuarial Journal, 17(2), 101-113.

Examples

data(XtriangleBDCL)

Plot.triangle(XtriangleBDCL)
# Classical chain ladder method
clm(XtriangleBDCL)

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/XtriangleBDCL.Rd_%03d_medium.png", width=480, height=480)
> ### Name: XtriangleBDCL
> ### Title: Paid data (BDCL example)
> ### Aliases: XtriangleBDCL
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(XtriangleBDCL)
> 
> Plot.triangle(XtriangleBDCL)
> # Classical chain ladder method
> clm(XtriangleBDCL)
$triangle.hat
             V1       V2         V3         V4         V5        V6         V7
 [1,]  125121.2   688995   612973.7   557602.6   426181.6  189655.2   86350.97
 [2,]  245098.7  1349666  1200748.2  1092282.3   834842.9  371513.6  169152.06
 [3,]  358431.7  1973747  1755970.7  1597350.4  1220871.9  543300.4  247367.48
 [4,]  476871.0  2625947  2336209.8  2125175.4  1624294.1  722827.4  329107.05
 [5,]  737493.1  4061094  3613007.2  3286637.2  2512011.7 1117870.8  508972.33
 [6,]  905736.4  4987546  4437238.0  4036413.6  3085073.7 1372889.3  625083.54
 [7,] 1320504.3  7271515  6469202.1  5884826.4  4497835.2 2001582.6  911330.83
 [8,] 1598988.5  8805022  7833506.9  7125890.9  5446393.9 2423700.9 1103523.46
 [9,] 1706637.5  9397804  8360883.5  7605628.6  5813062.5 2586872.1 1177816.17
[10,] 1672442.9  9209507  8193363.1  7453240.6  5696590.8 2535041.0 1154217.20
[11,] 1758663.4  9684291  8615760.5  7837482.0  5990270.6 2665731.5 1213721.26
[12,] 1618476.7  8912336  7928980.4  7212740.1  5512773.8 2453240.6 1116973.03
[13,] 1408909.5  7758329  6902302.4  6278803.9  4798956.4 2135584.5  972342.62
[14,] 1766462.4  9727237  8653968.2  7872238.3  6016835.2 2677553.0 1219103.66
[15,] 1943769.5 10703600  9522602.7  8662407.4  6620769.8 2946310.1 1341470.12
[16,] 2216071.8 12203065 10856622.1  9875922.2  7548272.1 3359058.1 1529396.40
[17,] 1942438.6 10696271  9516082.5  8656476.2  6616236.5 2944292.7 1340551.61
[18,] 2843966.6 15660642 13932703.0 12674134.7  9686975.5 4310802.9 1962730.72
[19,] 4664157.0 25683739 22849886.7 20785811.8 15886816.3 7069795.3 3218914.14
              V8        V9        V10        V11        V12        V13
 [1,]   40413.81  13570.30   9803.112   3671.692   6664.635   6073.573
 [2,]   79166.22  26582.72  19203.219   7192.441  13055.287  11897.462
 [3,]  115772.44  38874.49  28082.731  10518.205  19092.014  17398.814
 [4,]  154028.04  51720.10  37362.328  13993.817  25400.737  23148.040
 [5,]  238208.23  79986.43  57781.779  21641.790  39282.879  35799.026
 [6,]  292550.38  98233.63  70963.463  26578.905  48244.432  43965.812
 [7,]  426519.27 143218.20 103460.078  38750.301  70337.220  64099.273
 [8,]  516468.90 173421.81 125279.010  46922.440  85170.796  77617.314
 [9,]  551239.23 185097.12 133713.192  50081.408  90904.766  82842.759
[10,]  540194.48 181388.48 131034.087  49077.967  89083.379  81182.904
[11,]  568043.45 190739.71 137789.366  51608.113  93675.948  85368.175
[12,]  522763.54 175535.45 126805.891  47494.324  86208.845  78563.302
[13,]  455073.90 152806.38 110386.526  41344.557  75046.157  68390.592
[14,]  570562.52 191585.57 138400.411  51836.976  94091.366  85746.752
[15,]  627832.23 210815.80 152292.230  57040.067 103535.704  94353.507
[16,]  715785.12 240348.94 173626.818  65030.798 118040.000 107571.470
[17,]  627402.35 210671.45 152187.955  57001.011 103464.813  94288.902
[18,]  918593.40 308448.65 222821.690  83456.418 151485.079 138050.429
[19,] 1506509.91 505861.40 365431.630 136870.046 248438.289 226405.219
             V14       V15        V16 V17 V18 V19
 [1,]   8304.046  1845.507   2937.050   0   0   0
 [2,]  16266.714  3615.146   5753.358   0   0   0
 [3,]  23788.395  5286.778   8413.694   0   0   0
 [4,]  31648.980  7033.730  11193.897   0   0   0
 [5,]  48945.944 10877.840  17311.643   0   0   0
 [6,]  60111.920 13359.387  21260.927   0   0   0
 [7,]  87639.240 19477.111  30997.038   0   0   0
 [8,] 106121.678 23584.684  37534.073   0   0   0
 [9,] 113266.128 25172.480  40060.987   0   0   0
[10,] 110996.704 24668.119  39258.317   0   0   0
[11,] 116718.984 25939.849  41282.224   0   0   0
[12,] 107415.073 23872.130  37991.533   0   0   0
[13,]  93506.513 20781.065  33072.228   0   0   0
[14,] 117236.589 26054.883  41465.296   0   0   0
[15,] 129004.109 28670.119  45627.338   0   0   0
[16,] 147076.269 32686.510  52019.263   0   0   0
[17,] 128915.780 28650.488  45596.097   0   0   0
[18,] 188748.392 41947.802  66758.236   0   0   0
[19,] 309550.801 68795.159 109484.723   0   0   0

$alpha
 [1]   2780164   5446036   7964267  10595962  16386922  20125249  29341294
 [8]  35529147  37921082  37161287  39077086  35962171  31305636  39250378
[15]  43190100  49240593  43160528  63192266 103636467

$beta
 [1] 0.0450049787 0.2478253026 0.2204811425 0.2005646499 0.1532936880
 [6] 0.0682172551 0.0310596668 0.0145364846 0.0048811139 0.0035260911
[11] 0.0013206746 0.0023972092 0.0021846096 0.0029868907 0.0006638123
[16] 0.0010564305 0.0000000000 0.0000000000 0.0000000000

$Fj
      V2       V3       V4       V5       V6       V7       V8       V9 
6.506620 1.752931 1.390727 1.214734 1.078667 1.033205 1.015041 1.004976 
     V10      V11      V12      V13      V14      V15      V16      V17 
1.003577 1.001335 1.002420 1.002200 1.003001 1.000665 1.001058 1.000000 
     V18      V19 
1.000000 1.000000 

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