Number of reported claims (BDCL example)

Description

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

Usage

data(NtriangleBDCL)

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(NtriangleBDCL)

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

# Classical chain ladder method
clm(NtriangleBDCL)

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/NtriangleBDCL.Rd_%03d_medium.png", width=480, height=480)
> ### Name: NtriangleBDCL
> ### Title: Number of reported claims (BDCL example)
> ### Aliases: NtriangleBDCL
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(NtriangleBDCL)
> 
> Plot.triangle(NtriangleBDCL, Histogram=TRUE)
> Plot.triangle(NtriangleBDCL)
> 
> # Classical chain ladder method
> clm(NtriangleBDCL)
$triangle.hat
             V1        V2        V3        V4        V5       V6        V7
 [1,]  819.2061  226.0447  20.42149  6.891826  1.756423 1.055017 0.9825767
 [2,] 1436.2705  396.3122  35.80391 12.083071  3.079443 1.849705 1.7226994
 [3,] 1570.0184  433.2174  39.13803 13.208267  3.366206 2.021953 1.8831201
 [4,] 1788.1188  493.3982  44.57493 15.043103  3.833825 2.302834 2.1447152
 [5,] 2291.1934  632.2123  57.11577 19.275375  4.912445 2.950720 2.7481158
 [6,] 2832.5369  781.5860  70.61059 23.829595  6.073115 3.647891 3.3974170
 [7,] 3843.3430 1060.4991  95.80836 32.333314  8.240339 4.949661 4.6098035
 [8,] 4926.6063 1359.4055 122.81237 41.446602 10.562915 6.344745 5.9090970
 [9,] 5872.3300 1620.3604 146.38774 49.402796 12.590599 7.562698 7.0434222
[10,] 5421.6580 1496.0059 135.15322 45.611378 11.624333 6.982299 6.5028747
[11,] 5561.5959 1534.6191 138.64164 46.788649 11.924368 7.162518 6.6707198
[12,] 4675.1293 1290.0151 116.54345 39.330974 10.023734 6.020879 5.6074692
[13,] 3983.5484 1099.1862  99.30345 33.512835  8.540947 5.130225 4.7779694
[14,] 4673.5574 1289.5814 116.50427 39.317750 10.020364 6.018855 5.6055838
[15,] 5340.7891 1473.6916 133.13728 44.931044 11.450946 6.878151 6.4058785
[16,] 5110.4711 1410.1396 127.39583 42.993422 10.957131 6.581536 6.1296292
[17,] 3997.3561 1102.9962  99.64766 33.628997  8.570551 5.148007 4.7945308
[18,] 4460.2710 1230.7290 111.18738 37.523412  9.563066 5.744173 5.3497627
[19,] 4524.0000 1248.3138 112.77604 38.059552  9.699705 5.826247 5.4262008
            V8        V9       V10       V11        V12        V13 V14
 [1,] 0.758561 0.3604582 0.1595790 0.1613905 0.04199486 0.05618433   0
 [2,] 1.329945 0.6319722 0.2797813 0.2829574 0.07362736 0.09850499   0
 [3,] 1.453791 0.6908225 0.3058350 0.3093069 0.08048366 0.10767795   0
 [4,] 1.655746 0.7867887 0.3483203 0.3522745 0.09166411 0.12263611   0
 [5,] 2.121578 1.0081461 0.4463178 0.4513844 0.11745317 0.15713892   0
 [6,] 2.622847 1.2463423 0.5517700 0.5580337 0.14520399 0.19426635   0
 [7,] 3.558824 1.6911062 0.7486720 0.7571710 0.19702082 0.26359135   0
 [8,] 4.561894 2.1677520 0.9596886 0.9705830 0.25255201 0.33788574   0
 [9,] 5.437607 2.5838791 1.1439128 1.1568986 0.30103253 0.40274713   0
[10,] 5.020298 2.3855793 1.0561232 1.0681124 0.27792979 0.37183830   0
[11,] 5.149876 2.4471533 1.0833827 1.0956813 0.28510341 0.38143579   0
[12,] 4.329034 2.0570998 0.9107016 0.9210399 0.23966058 0.32063847   0
[13,] 3.688650 1.7527979 0.7759836 0.7847926 0.20420815 0.27320717   0
[14,] 4.327578 2.0564082 0.9103954 0.9207302 0.23958000 0.32053066   0
[15,] 4.945415 2.3499963 1.0403702 1.0521805 0.27378422 0.36629200   0
[16,] 4.732148 2.2486542 0.9955049 1.0068059 0.26197746 0.35049590   0
[17,] 3.701435 1.7588734 0.7786733 0.7875129 0.20491598 0.27415416   0
[18,] 4.130081 1.9625602 0.8688478 0.8787110 0.22864633 0.30590266   0
[19,] 4.189092 1.9906015 0.8812620 0.8912662 0.23191326 0.31027344   0
            V15 V16 V17 V18 V19
 [1,] 0.1036339   0   0   0   0
 [2,] 0.1816958   0   0   0   0
 [3,] 0.1986157   0   0   0   0
 [4,] 0.2262065   0   0   0   0
 [5,] 0.2898481   0   0   0   0
 [6,] 0.3583309   0   0   0   0
 [7,] 0.4862032   0   0   0   0
 [8,] 0.6232418   0   0   0   0
 [9,] 0.7428809   0   0   0   0
[10,] 0.6858685   0   0   0   0
[11,] 0.7035713   0   0   0   0
[12,] 0.5914286   0   0   0   0
[13,] 0.5039400   0   0   0   0
[14,] 0.5912298   0   0   0   0
[15,] 0.6756381   0   0   0   0
[16,] 0.6465017   0   0   0   0
[17,] 0.5056867   0   0   0   0
[18,] 0.5642479   0   0   0   0
[19,] 0.5723100   0   0   0   0

$alpha
 [1] 1078.000 1890.000 2066.000 2353.000 3015.000 3727.358 5057.486 6482.961
 [9] 7727.447 7134.404 7318.549 6152.041 5241.984 6149.972 7027.988 6724.910
[17] 5260.153 5869.307 5953.168

$beta
 [1] 7.599315e-01 2.096890e-01 1.894387e-02 6.393159e-03 1.629335e-03
 [6] 9.786800e-04 9.114812e-04 7.036744e-04 3.343768e-04 1.480324e-04
[11] 1.497129e-04 3.895627e-05 5.211904e-05 0.000000e+00 9.613536e-05
[16] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00

$Fj
      V2       V3       V4       V5       V6       V7       V8       V9 
1.275931 1.019537 1.006467 1.001638 1.000982 1.000914 1.000705 1.000335 
     V10      V11      V12      V13      V14      V15      V16      V17 
1.000148 1.000150 1.000039 1.000052 1.000000 1.000096 1.000000 1.000000 
     V18      V19 
1.000000 1.000000 

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