diff --git a/articles/ChainLadder.html b/articles/ChainLadder.html index 553313b..c57721f 100644 --- a/articles/ChainLadder.html +++ b/articles/ChainLadder.html @@ -918,23 +918,23 @@

Bootstrap chain-ladder +Mean Ultimate: 214,180 +Mean IBNR: 53,193 +IBNR.S.E 18,472 +Total IBNR 75%: 63,315 +Total IBNR 95%: 87,646

You can use summary(B)$ByOrigin and summary(B)$Totals to extract the information from the output above.

@@ -948,22 +948,22 @@

Bootstrap chain-ladder$ByOrigin IBNR 75% IBNR 95% IBNR 99% IBNR 99.5% 1981 0.0 0 0 0 -1982 205.6 1379 2671 3725 -1983 1093.6 3235 5711 5921 -1984 2747.0 5647 7908 8928 -1985 4267.0 7346 11476 12510 -1986 5174.7 8108 10723 11830 -1987 7352.2 11636 14363 15597 -1988 13972.0 20105 24219 24647 -1989 14490.2 22398 28102 31133 -1990 25900.5 43973 56774 62404 +1982 158.3 1497 2881 3330 +1983 1117.4 3132 5894 7145 +1984 2603.5 4845 7662 8384 +1985 4174.9 7142 9897 10930 +1986 5122.6 8207 10509 11985 +1987 7101.9 11445 15008 16167 +1988 13998.2 20411 25434 26114 +1989 14252.2 22086 29634 32392 +1990 23678.3 39414 56188 63437 $Totals Totals -IBNR 75%: 65945 -IBNR 95%: 89208 -IBNR 99%: 111319 -IBNR 99.5%: 115124 +IBNR 75%: 63315 +IBNR 95%: 87646 +IBNR 99%: 104712 +IBNR 99.5%: 111788

The distribution of the IBNR appears to follow a log-normal distribution, so let’s fit it:

 -
   meanlog     sdlog  
-  10.84563    0.36878 
- ( 0.01167) ( 0.00825)
+
    meanlog      sdlog  
+  10.819039    0.364721 
+ ( 0.011539) ( 0.008159)
 curve(plnorm(x,fit$estimate["meanlog"], fit$estimate["sdlog"]),
       col="red", add=TRUE)
diff --git a/articles/ChainLadder_files/figure-html/multi-1.png b/articles/ChainLadder_files/figure-html/multi-1.png index db80ebf..708fcbc 100644 Binary files a/articles/ChainLadder_files/figure-html/multi-1.png and b/articles/ChainLadder_files/figure-html/multi-1.png differ diff --git a/articles/ChainLadder_files/figure-html/unnamed-chunk-30-1.png b/articles/ChainLadder_files/figure-html/unnamed-chunk-30-1.png index 9e32846..c936f7a 100644 Binary files a/articles/ChainLadder_files/figure-html/unnamed-chunk-30-1.png and b/articles/ChainLadder_files/figure-html/unnamed-chunk-30-1.png differ diff --git a/articles/ChainLadder_files/figure-html/unnamed-chunk-32-1.png b/articles/ChainLadder_files/figure-html/unnamed-chunk-32-1.png index b98dd2d..e0a8cd8 100644 Binary files a/articles/ChainLadder_files/figure-html/unnamed-chunk-32-1.png and b/articles/ChainLadder_files/figure-html/unnamed-chunk-32-1.png differ diff --git a/pkgdown.yml b/pkgdown.yml index 5b6a3bf..4802b3f 100644 --- a/pkgdown.yml +++ b/pkgdown.yml @@ -3,7 +3,7 @@ pkgdown: 2.0.7 pkgdown_sha: ~ articles: ChainLadder: ChainLadder.html -last_built: 2023-06-27T11:18Z +last_built: 2023-06-27T11:25Z urls: reference: http://mages.github.io/ChainLadder/reference article: http://mages.github.io/ChainLadder/articles diff --git a/reference/BootChainLadder-1.png b/reference/BootChainLadder-1.png index e2847bd..302359d 100644 Binary files a/reference/BootChainLadder-1.png and b/reference/BootChainLadder-1.png differ diff --git a/reference/BootChainLadder-2.png b/reference/BootChainLadder-2.png index a7a0930..a9be2ac 100644 Binary files a/reference/BootChainLadder-2.png and b/reference/BootChainLadder-2.png differ diff --git a/reference/BootChainLadder-3.png b/reference/BootChainLadder-3.png index 8ce8b10..8e78dfb 100644 Binary files a/reference/BootChainLadder-3.png and b/reference/BootChainLadder-3.png differ diff --git a/reference/BootChainLadder.html b/reference/BootChainLadder.html index 3cc1b80..0afc9fe 100644 --- a/reference/BootChainLadder.html +++ b/reference/BootChainLadder.html @@ -170,23 +170,23 @@

Examples#> #> Latest Mean Ultimate Mean IBNR IBNR.S.E IBNR 75% IBNR 95% #> 1981 18,834 18,834 0 0 0 0 -#> 1982 16,704 16,905 201 739 249 1,469 -#> 1983 23,466 24,190 724 1,348 1,157 3,330 -#> 1984 27,067 28,814 1,747 1,895 2,661 5,489 -#> 1985 26,180 29,060 2,880 2,369 4,021 7,214 -#> 1986 15,852 19,657 3,805 2,460 5,118 8,403 -#> 1987 12,314 17,868 5,554 3,096 7,286 11,289 -#> 1988 13,112 24,339 11,227 5,002 14,354 20,653 -#> 1989 5,395 16,413 11,018 6,068 14,400 22,123 -#> 1990 2,063 19,238 17,175 13,779 24,541 42,579 +#> 1982 16,704 16,856 152 765 173 1,319 +#> 1983 23,466 24,164 698 1,353 1,189 3,312 +#> 1984 27,067 28,719 1,652 1,974 2,520 5,318 +#> 1985 26,180 28,980 2,800 2,374 4,085 6,984 +#> 1986 15,852 19,535 3,683 2,488 5,045 8,241 +#> 1987 12,314 17,813 5,499 3,184 7,152 11,387 +#> 1988 13,112 24,147 11,035 4,722 13,783 19,191 +#> 1989 5,395 16,101 10,706 6,128 14,221 21,047 +#> 1990 2,063 18,476 16,413 13,953 23,580 41,967 #> #> Totals #> Latest: 160,987 -#> Mean Ultimate: 215,320 -#> Mean IBNR: 54,333 -#> IBNR.S.E 18,978 -#> Total IBNR 75%: 66,265 -#> Total IBNR 95%: 88,400 +#> Mean Ultimate: 213,623 +#> Mean IBNR: 52,636 +#> IBNR.S.E 18,858 +#> Total IBNR 75%: 63,389 +#> Total IBNR 95%: 86,853 plot(B) # Compare to MackChainLadder @@ -216,22 +216,22 @@

Examples#> $ByOrigin #> IBNR 75% IBNR 95% IBNR 99% IBNR 99.5% #> 1981 0.0000 0.000 0.000 0.000 -#> 1982 248.8583 1468.960 2883.723 3622.207 -#> 1983 1157.3411 3330.256 5277.488 6293.166 -#> 1984 2660.6216 5488.945 7413.201 7938.333 -#> 1985 4020.5285 7213.827 9994.209 12099.349 -#> 1986 5117.6374 8403.303 11335.161 12693.448 -#> 1987 7285.9166 11288.732 14610.828 16366.046 -#> 1988 14354.1291 20652.588 23783.535 24767.326 -#> 1989 14400.0746 22122.701 28344.433 30481.118 -#> 1990 24540.8496 42578.927 58208.632 67289.885 +#> 1982 172.5145 1319.019 2720.804 3458.285 +#> 1983 1189.2271 3311.772 5579.535 6907.461 +#> 1984 2519.5002 5317.966 8067.925 9151.914 +#> 1985 4084.5696 6983.915 9530.828 11525.360 +#> 1986 5044.6494 8241.448 11290.725 12267.884 +#> 1987 7151.7259 11387.021 14733.680 16138.524 +#> 1988 13782.5485 19191.469 24842.843 25499.711 +#> 1989 14221.2148 21047.373 28659.805 30934.371 +#> 1990 23580.4642 41966.521 59278.324 65709.160 #> #> $Totals #> Totals -#> IBNR 75%: 66265.15 -#> IBNR 95%: 88399.73 -#> IBNR 99%: 105551.36 -#> IBNR 99.5%: 114552.67 +#> IBNR 75%: 63389.48 +#> IBNR 95%: 86852.96 +#> IBNR 99%: 104920.31 +#> IBNR 99.5%: 109578.24 #> # fit a distribution to the IBNR @@ -241,8 +241,8 @@

Examplesfit <- fitdistr(B$IBNR.Totals[B$IBNR.Totals>0], "lognormal") fit #> meanlog sdlog -#> 10.839279384 0.367486778 -#> ( 0.011626767) ( 0.008221366) +#> 10.806142410 0.369971669 +#> ( 0.011705386) ( 0.008276958) curve(plnorm(x,fit$estimate["meanlog"], fit$estimate["sdlog"]), col="red", add=TRUE) @@ -253,24 +253,24 @@

Examples#> #> Latest Mean Ultimate Mean IBNR IBNR.S.E IBNR 75% IBNR 95% #> 1977 762,544 762,544 0 0 0 0 -#> 1978 889,022 903,760 14,738 5,204 17,627 25,003 -#> 1979 1,019,932 1,057,985 38,053 7,864 42,918 52,027 -#> 1980 1,002,134 1,066,163 64,029 10,035 70,851 81,020 -#> 1981 1,002,194 1,102,823 100,629 11,954 108,607 120,840 -#> 1982 944,614 1,088,901 144,287 13,856 153,201 168,044 -#> 1983 895,700 1,107,648 211,948 17,629 222,327 242,996 -#> 1984 1,024,228 1,410,200 385,972 23,896 402,025 425,819 -#> 1985 1,173,448 1,937,777 764,329 37,584 789,821 827,902 -#> 1986 1,011,178 2,373,777 1,362,599 58,258 1,400,107 1,463,125 -#> 1987 496,200 2,688,305 2,192,105 115,763 2,268,209 2,390,095 +#> 1978 889,022 903,697 14,675 5,241 17,859 24,252 +#> 1979 1,019,932 1,057,376 37,444 8,402 42,598 52,396 +#> 1980 1,002,134 1,065,711 63,577 9,547 70,338 79,561 +#> 1981 1,002,194 1,102,423 100,229 12,148 108,271 119,779 +#> 1982 944,614 1,088,756 144,142 13,903 153,691 168,090 +#> 1983 895,700 1,107,640 211,940 17,082 223,747 239,858 +#> 1984 1,024,228 1,410,182 385,954 25,538 402,746 429,048 +#> 1985 1,173,448 1,937,546 764,098 37,446 786,384 827,824 +#> 1986 1,011,178 2,368,897 1,357,719 61,094 1,398,033 1,460,880 +#> 1987 496,200 2,685,362 2,189,162 111,139 2,262,999 2,384,063 #> #> Totals #> Latest: 10,221,194 -#> Mean Ultimate: 15,499,883 -#> Mean IBNR: 5,278,689 -#> IBNR.S.E 174,590 -#> Total IBNR 75%: 5,394,975 -#> Total IBNR 95%: 5,578,210 +#> Mean Ultimate: 15,490,135 +#> Mean IBNR: 5,268,941 +#> IBNR.S.E 177,978 +#> Total IBNR 75%: 5,390,184 +#> Total IBNR 95%: 5,575,855 plot(A, log=TRUE) @@ -278,17 +278,17 @@

ExamplesCDR(A) #> IBNR IBNR.S.E CDR(1)S.E CDR(1)75% CDR(1)95% #> 1977 0.00 0.000 0.000 0.00 0.00 -#> 1978 14738.19 5203.627 5203.627 17627.04 25002.61 -#> 1979 38053.38 7863.520 6256.790 41881.51 49088.94 -#> 1980 64028.95 10034.868 7058.528 68645.81 76414.63 -#> 1981 100629.38 11954.041 7744.934 105314.95 113848.05 -#> 1982 144287.49 13856.275 8914.553 150081.46 160464.02 -#> 1983 211947.53 17629.462 10345.482 218513.20 229685.14 -#> 1984 385972.15 23896.268 15486.176 396214.96 412122.75 -#> 1985 764328.51 37583.680 25560.458 783708.92 807566.42 -#> 1986 1362598.88 58257.911 42333.067 1392392.21 1435639.73 -#> 1987 2192104.53 115763.134 96583.137 2255955.66 2353906.36 -#> Total 5278689.00 174589.793 133198.035 5369340.62 5505316.98 +#> 1978 14675.43 5240.773 5240.773 17859.39 24251.66 +#> 1979 37443.83 8401.608 6575.957 41679.44 49325.03 +#> 1980 63576.88 9547.144 6804.844 68061.96 75237.40 +#> 1981 100229.40 12147.574 8093.141 105375.16 113929.93 +#> 1982 144142.28 13902.644 9041.151 150362.51 160139.64 +#> 1983 211940.12 17082.273 10521.331 218687.33 230191.93 +#> 1984 385953.86 25537.810 15523.142 396119.26 412833.41 +#> 1985 764098.41 37445.699 25748.187 782400.65 805524.55 +#> 1986 1357718.84 61094.314 43677.035 1388920.19 1434123.74 +#> 1987 2189161.82 111138.869 90227.304 2244170.54 2350701.76 +#> Total 5268940.88 177978.087 135340.603 5357963.63 5504182.20 diff --git a/reference/CDR.html b/reference/CDR.html index 71a5d0a..0f50ff9 100644 --- a/reference/CDR.html +++ b/reference/CDR.html @@ -250,34 +250,34 @@

Examples#> #> Latest Mean Ultimate Mean IBNR IBNR.S.E IBNR 75% IBNR 95% #> 1 3,678,633 3,678,633 0 0 0 0 -#> 2 3,902,425 3,906,906 4,481 5,914 7,088 15,579 -#> 3 3,898,825 3,908,363 9,538 8,206 13,166 25,181 -#> 4 3,548,422 3,577,378 28,956 11,972 36,160 49,394 -#> 5 3,585,812 3,636,856 51,044 15,212 61,250 76,495 -#> 6 3,641,036 3,753,924 112,888 22,795 128,105 151,854 -#> 7 3,428,335 3,615,534 187,199 29,056 205,828 238,847 -#> 8 3,158,581 3,571,794 413,213 45,365 441,674 487,259 -#> 9 2,144,738 3,579,606 1,434,868 97,334 1,497,136 1,598,878 +#> 2 3,902,425 3,907,039 4,614 5,993 6,815 16,154 +#> 3 3,898,825 3,908,757 9,932 7,931 13,990 24,169 +#> 4 3,548,422 3,576,974 28,552 11,893 35,652 49,619 +#> 5 3,585,812 3,637,585 51,773 15,762 61,044 78,989 +#> 6 3,641,036 3,753,948 112,912 22,726 127,750 153,136 +#> 7 3,428,335 3,616,699 188,364 28,440 206,214 235,872 +#> 8 3,158,581 3,570,454 411,873 43,926 440,675 487,910 +#> 9 2,144,738 3,574,752 1,430,014 96,243 1,492,538 1,583,005 #> #> Totals #> Latest: 30,986,807 -#> Mean Ultimate: 33,228,993 -#> Mean IBNR: 2,242,186 -#> IBNR.S.E 131,627 -#> Total IBNR 75%: 2,329,963 -#> Total IBNR 95%: 2,465,662 +#> Mean Ultimate: 33,224,841 +#> Mean IBNR: 2,238,034 +#> IBNR.S.E 130,864 +#> Total IBNR 75%: 2,325,604 +#> Total IBNR 95%: 2,452,894 CDR(B) #> IBNR IBNR.S.E CDR(1)S.E CDR(1)75% CDR(1)95% #> 1 0.000 0.000 0.000 0.00 0.00 -#> 2 4481.462 5913.824 5913.824 7087.50 15579.30 -#> 3 9538.082 8206.174 6191.439 12701.67 20885.04 -#> 4 28955.805 11971.889 10128.473 34916.54 46885.52 -#> 5 51043.614 15211.554 10379.756 57825.94 69637.97 -#> 6 112887.806 22795.380 16800.600 122853.51 143691.33 -#> 7 187199.262 29056.397 19594.769 201239.35 220538.26 -#> 8 413212.592 45364.551 34270.554 435431.01 469674.69 -#> 9 1434867.599 97333.965 86820.525 1487562.19 1582937.84 -#> Total 2242186.221 131627.488 109916.488 2307573.69 2426134.35 +#> 2 4613.529 5992.835 5992.835 6815.00 16154.20 +#> 3 9931.599 7931.072 6323.540 13174.97 21577.41 +#> 4 28551.810 11892.895 9695.777 34050.56 45714.43 +#> 5 51773.322 15761.605 10612.276 57360.38 69524.31 +#> 6 112911.999 22725.889 16730.014 122743.84 142208.18 +#> 7 188364.495 28440.125 19466.625 199971.76 220832.36 +#> 8 411873.245 43926.384 34243.679 433217.98 471453.04 +#> 9 1430013.654 96242.623 87487.988 1484848.61 1572324.28 +#> Total 2238033.653 130863.625 112313.117 2311938.03 2416044.62