data.loss.XL: US Casualty data, XL Group
In apc: Age-Period-Cohort Analysis
Description
Usage
Value
Author(s)
Source
References
See Also
Examples
View source: R/apc_data_sets.R
Description
Function that organises US Casualty data from XL Group in apc.data.list format.
The data set is taken from table 1.1 Kuang and Nielsen (2020).
Data are for US Casualty data from the XL Group.
They are gross paid and reported loss and allocated loss adjustment expense in 1000 USD.
The data set is in "CL"-format.
Usage
1
Value
The value is a list in apc.data.list format.
response
matrix of paid amounts, incremental
dose
NULL.
data.format
logical. Equal to "CL".
age1
numeric. Equal to 1.
per1
NULL. Not needed when data.format="CL"
coh1
numeric. Equal to 1997.
unit
numeric. Equal to 1997.
per.zero
NULL. Not needed when data.format="CL"
per.max
NULL. Not needed when data.format="CL"
time.adjust
-1996. Thus age=1 in cohort=1997 corresponds to period=1997+1997-1+(-1996)=1997.
label
character. "loss, US casualty, XL Group".
Author(s)
Bent Nielsen <bent.nielsen@nuffield.ox.ac.uk> 26 August 2020 (10 Mar 2018)
Source
Table 1.1 of Kuang and Nielsen (2020) and in turn
download:
xls file
from
XL Group files.
References
Kuang, D. and Nielsen B. (2020) Generalized log-normal chain-ladder. Scandinavian Actuarial Journal 2020, 553-576. Download: Open access. Earlier version: Nuffield DP.
See Also
General description of apc.data.list format.
For explanation for Chain Ladder forecast, see apc.forecast.ac.
The analysis in Kuang and Nielsen (2020) is reproduced in the vignette
ReproducingKN2020.pdf,
ReproducingKN2020.R
on
Vignettes.
Examples
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#########################
## It is convenient to construct a data variable for paid data
data <- data.loss.XL()
## To see the content of the data
data
#########################
# Get deviance table.
# reproduce Table 4.1 in Kuang and Nielsen (2018).
apc.fit.table(data,"log.normal.response")
apc.fit.table(data,"log.normal.response",model.design.reference="AC")
#########################
# > apc.fit.table(data,"log.normal.response")
# -2logL df.residual LR vs.APC df vs.APC prob(>chi_sq) F vs.APC prob(>F) aic
# APC 170.003 153 NaN NaN NaN NaN NaN 286.003
# AP 243.531 171 73.527 18 0.000 3.564 0.000 323.531
# AC 179.873 171 9.869 18 0.936 0.409 0.984 259.873
# PC 633.432 171 463.428 18 0.000 68.736 0.000 713.432
# Ad 258.570 189 88.567 36 0.000 2.230 0.000 302.570
# Pd 643.892 189 473.888 36 0.000 36.340 0.000 687.892
# Cd 649.142 189 479.139 36 0.000 37.368 0.000 693.142
# A 357.359 190 187.355 37 0.000 5.956 0.000 399.359
# P 644.176 190 474.172 37 0.000 35.412 0.000 686.176
# C 672.392 190 502.388 37 0.000 41.099 0.000 714.392
# t 664.488 207 494.484 54 0.000 27.015 0.000 672.488
# tA 681.993 208 511.989 55 0.000 29.072 0.000 687.993
# tP 664.746 208 494.742 55 0.000 26.560 0.000 670.746
# tC 686.181 208 516.178 55 0.000 29.713 0.000 692.181
# 1 690.399 209 520.396 56 0.000 29.830 0.000 694.399
#
# > apc.fit.table(data,"log.normal.response",model.design.reference="AC")
# -2logL df.residual LR vs.AC df vs.AC prob(>chi_sq) F vs.AC prob(>F) aic
# AC 179.873 171 NaN NaN NaN NaN NaN 259.873
# Ad 258.570 189 78.698 18 0 4.319 0 302.570
# Cd 649.142 189 469.269 18 0 79.257 0 693.142
# A 357.359 190 177.486 19 0 11.955 0 399.359
# C 672.392 190 492.519 19 0 84.930 0 714.392
# t 664.488 207 484.615 36 0 42.993 0 672.488
# tA 681.993 208 502.120 37 0 45.869 0 687.993
# tC 686.181 208 506.308 37 0 46.886 0 692.181
# 1 690.399 209 510.526 38 0 46.670 0 694.399
#########################
# Fit log normal chain-ladder model
# reproduce Table 4.2 in Kuang and Nielsen (2018).
fit.ac <- apc.fit.model(data,"log.normal.response","AC")
id.ac <- apc.identify(fit.ac)
id.ac$coefficients.dif
fit.ac$s2
fit.ac$RSS
#########################
# > id.ac$coefficients.dif
# Estimate Std. Error t value Pr(>|t|)
# level 7.660055032 0.1377951 55.59016605 0.000000e+00
# D_age_1998 2.272100342 0.1335080 17.01846386 5.992216e-65
# D_age_1999 0.932530550 0.1362610 6.84370899 7.716860e-12
# D_age_2000 0.235606356 0.1398301 1.68494782 9.199864e-02
# D_age_2001 0.088886609 0.1438733 0.61781154 5.366996e-01
# D_age_2002 -0.176044303 0.1483681 -1.18653717 2.354102e-01
# D_age_2003 -0.144445459 0.1533567 -0.94189218 3.462478e-01
# D_age_2004 -0.427608601 0.1589136 -2.69082462 7.127565e-03
# D_age_2005 -0.300527594 0.1651428 -1.81980421 6.878883e-02
# D_age_2006 -0.399729999 0.1721838 -2.32153023 2.025824e-02
# D_age_2007 -0.189656058 0.1802245 -1.05233225 2.926471e-01
# D_age_2008 -0.242063670 0.1895226 -1.27722853 2.015216e-01
# D_age_2009 -0.260459607 0.2004421 -1.29942545 1.937980e-01
# D_age_2010 -0.555317528 0.2135164 -2.60081872 9.300158e-03
# D_age_2011 -0.303234088 0.2295651 -1.32090683 1.865324e-01
# D_age_2012 0.405830766 0.2499291 1.62378389 1.044219e-01
# D_age_2013 -0.895278068 0.2769988 -3.23206421 1.228994e-03
# D_age_2014 0.116668873 0.3156054 0.36966685 7.116307e-01
# D_age_2015 -0.383048241 0.3777268 -1.01408813 3.105407e-01
# D_age_2016 -0.273419402 0.5083832 -0.53782152 5.907003e-01
# D_cohort_1998 0.288755900 0.1335080 2.16283663 3.055375e-02
# D_cohort_1999 0.163424236 0.1362610 1.19934721 2.303930e-01
# D_cohort_2000 -0.264981486 0.1398301 -1.89502518 5.808907e-02
# D_cohort_2001 0.149829430 0.1438733 1.04139815 2.976908e-01
# D_cohort_2002 -0.374386828 0.1483681 -2.52336417 1.162380e-02
# D_cohort_2003 -0.198735893 0.1533567 -1.29590632 1.950078e-01
# D_cohort_2004 -0.008807130 0.1589136 -0.05542087 9.558032e-01
# D_cohort_2005 -0.005337953 0.1651428 -0.03232325 9.742143e-01
# D_cohort_2006 -0.132272851 0.1721838 -0.76820710 4.423642e-01
# D_cohort_2007 -0.021862643 0.1802245 -0.12130783 9.034472e-01
# D_cohort_2008 -0.472602270 0.1895226 -2.49364600 1.264386e-02
# D_cohort_2009 -0.437572798 0.2004421 -2.18303804 2.903301e-02
# D_cohort_2010 0.295511564 0.2135164 1.38402260 1.663515e-01
# D_cohort_2011 0.310545832 0.2295651 1.35275725 1.761332e-01
# D_cohort_2012 -0.268692406 0.2499291 -1.07507473 2.823413e-01
# D_cohort_2013 0.142131410 0.2769988 0.51311192 6.078730e-01
# D_cohort_2014 0.201777590 0.3156054 0.63933494 5.226051e-01
# D_cohort_2015 -0.092672697 0.3777268 -0.24534320 8.061907e-01
# D_cohort_2016 0.872997251 0.5083832 1.71720334 8.594203e-02
# > fit.ac$s2
# [1] 0.1693316
# > fit.ac$RSS
# [1] 28.9557
# > fit.ac$RSS
forecast <- apc.forecast.ac(fit.ac,quantiles=c(0.995))
forecast$response.forecast.coh
#########################
# > forecast$response.forecast.coh
# forecast se se.proc se.est t-0.995
# coh_2 1871.073 1026.463 707.4405 743.7428 4544.891
# coh_3 5099.330 1874.681 1375.8435 1273.3744 9982.659
# coh_4 7171.317 2123.128 1622.5220 1369.3412 12701.822
# coh_5 11699.350 2984.949 2274.8292 1932.6338 19474.801
# coh_6 13717.388 3345.138 2654.4080 2035.6984 22431.090
# coh_7 14343.522 3188.410 2471.3130 2014.5886 22648.964
# coh_8 18377.001 3834.057 2910.9751 2495.2390 28364.281
# coh_9 25488.052 5241.618 3976.5389 3414.9225 39141.867
# coh_10 30524.942 6213.652 4662.3320 4107.5694 46710.794
# coh_11 40078.245 8115.990 5976.5789 5490.8835 61219.471
# coh_12 32680.319 6603.511 4727.4210 4610.6241 49881.712
# coh_13 28509.077 5895.265 4143.1332 4193.8760 43865.568
# coh_14 51760.526 11013.030 7540.3989 8026.7807 80448.208
# coh_15 98747.731 22063.641 14798.3216 16365.0210 156220.991
# coh_16 100330.677 23254.845 14704.7084 18015.5316 160906.889
# coh_17 149813.314 36629.836 21310.2885 29792.8931 245229.846
# coh_18 221549.649 58610.037 29815.3239 50459.7158 374222.093
# coh_19 229480.904 69931.745 29102.9866 63588.2473 411645.102
# coh_20 575343.178 235016.967 70362.1087 224236.8135 1187535.497
apc documentation built on Oct. 23, 2020, 6:17 p.m.
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Description Usage Value Author(s) Source References See Also Examples
View source: R/apc_data_sets.R
Description
Function that organises US Casualty data from XL Group in apc.data.list format.
The data set is taken from table 1.1 Kuang and Nielsen (2020). Data are for US Casualty data from the XL Group. They are gross paid and reported loss and allocated loss adjustment expense in 1000 USD.
The data set is in "CL"-format.
Usage
1 |
Value
The value is a list in apc.data.list format.
response |
matrix of paid amounts, incremental |
dose |
NULL. |
data.format |
logical. Equal to "CL". |
age1 |
numeric. Equal to 1. |
per1 |
NULL. Not needed when data.format="CL" |
coh1 |
numeric. Equal to 1997. |
unit |
numeric. Equal to 1997. |
per.zero |
NULL. Not needed when data.format="CL" |
per.max |
NULL. Not needed when data.format="CL" |
time.adjust |
-1996. Thus age=1 in cohort=1997 corresponds to period=1997+1997-1+(-1996)=1997. |
label |
character. "loss, US casualty, XL Group". |
Author(s)
Bent Nielsen <bent.nielsen@nuffield.ox.ac.uk> 26 August 2020 (10 Mar 2018)
Source
Table 1.1 of Kuang and Nielsen (2020) and in turn download: xls file from XL Group files.
References
Kuang, D. and Nielsen B. (2020) Generalized log-normal chain-ladder. Scandinavian Actuarial Journal 2020, 553-576. Download: Open access. Earlier version: Nuffield DP.
See Also
General description of apc.data.list format.
For explanation for Chain Ladder forecast, see apc.forecast.ac.
The analysis in Kuang and Nielsen (2020) is reproduced in the vignette
ReproducingKN2020.pdf,
ReproducingKN2020.R
on
Vignettes.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 | #########################
## It is convenient to construct a data variable for paid data
data <- data.loss.XL()
## To see the content of the data
data
#########################
# Get deviance table.
# reproduce Table 4.1 in Kuang and Nielsen (2018).
apc.fit.table(data,"log.normal.response")
apc.fit.table(data,"log.normal.response",model.design.reference="AC")
#########################
# > apc.fit.table(data,"log.normal.response")
# -2logL df.residual LR vs.APC df vs.APC prob(>chi_sq) F vs.APC prob(>F) aic
# APC 170.003 153 NaN NaN NaN NaN NaN 286.003
# AP 243.531 171 73.527 18 0.000 3.564 0.000 323.531
# AC 179.873 171 9.869 18 0.936 0.409 0.984 259.873
# PC 633.432 171 463.428 18 0.000 68.736 0.000 713.432
# Ad 258.570 189 88.567 36 0.000 2.230 0.000 302.570
# Pd 643.892 189 473.888 36 0.000 36.340 0.000 687.892
# Cd 649.142 189 479.139 36 0.000 37.368 0.000 693.142
# A 357.359 190 187.355 37 0.000 5.956 0.000 399.359
# P 644.176 190 474.172 37 0.000 35.412 0.000 686.176
# C 672.392 190 502.388 37 0.000 41.099 0.000 714.392
# t 664.488 207 494.484 54 0.000 27.015 0.000 672.488
# tA 681.993 208 511.989 55 0.000 29.072 0.000 687.993
# tP 664.746 208 494.742 55 0.000 26.560 0.000 670.746
# tC 686.181 208 516.178 55 0.000 29.713 0.000 692.181
# 1 690.399 209 520.396 56 0.000 29.830 0.000 694.399
#
# > apc.fit.table(data,"log.normal.response",model.design.reference="AC")
# -2logL df.residual LR vs.AC df vs.AC prob(>chi_sq) F vs.AC prob(>F) aic
# AC 179.873 171 NaN NaN NaN NaN NaN 259.873
# Ad 258.570 189 78.698 18 0 4.319 0 302.570
# Cd 649.142 189 469.269 18 0 79.257 0 693.142
# A 357.359 190 177.486 19 0 11.955 0 399.359
# C 672.392 190 492.519 19 0 84.930 0 714.392
# t 664.488 207 484.615 36 0 42.993 0 672.488
# tA 681.993 208 502.120 37 0 45.869 0 687.993
# tC 686.181 208 506.308 37 0 46.886 0 692.181
# 1 690.399 209 510.526 38 0 46.670 0 694.399
#########################
# Fit log normal chain-ladder model
# reproduce Table 4.2 in Kuang and Nielsen (2018).
fit.ac <- apc.fit.model(data,"log.normal.response","AC")
id.ac <- apc.identify(fit.ac)
id.ac$coefficients.dif
fit.ac$s2
fit.ac$RSS
#########################
# > id.ac$coefficients.dif
# Estimate Std. Error t value Pr(>|t|)
# level 7.660055032 0.1377951 55.59016605 0.000000e+00
# D_age_1998 2.272100342 0.1335080 17.01846386 5.992216e-65
# D_age_1999 0.932530550 0.1362610 6.84370899 7.716860e-12
# D_age_2000 0.235606356 0.1398301 1.68494782 9.199864e-02
# D_age_2001 0.088886609 0.1438733 0.61781154 5.366996e-01
# D_age_2002 -0.176044303 0.1483681 -1.18653717 2.354102e-01
# D_age_2003 -0.144445459 0.1533567 -0.94189218 3.462478e-01
# D_age_2004 -0.427608601 0.1589136 -2.69082462 7.127565e-03
# D_age_2005 -0.300527594 0.1651428 -1.81980421 6.878883e-02
# D_age_2006 -0.399729999 0.1721838 -2.32153023 2.025824e-02
# D_age_2007 -0.189656058 0.1802245 -1.05233225 2.926471e-01
# D_age_2008 -0.242063670 0.1895226 -1.27722853 2.015216e-01
# D_age_2009 -0.260459607 0.2004421 -1.29942545 1.937980e-01
# D_age_2010 -0.555317528 0.2135164 -2.60081872 9.300158e-03
# D_age_2011 -0.303234088 0.2295651 -1.32090683 1.865324e-01
# D_age_2012 0.405830766 0.2499291 1.62378389 1.044219e-01
# D_age_2013 -0.895278068 0.2769988 -3.23206421 1.228994e-03
# D_age_2014 0.116668873 0.3156054 0.36966685 7.116307e-01
# D_age_2015 -0.383048241 0.3777268 -1.01408813 3.105407e-01
# D_age_2016 -0.273419402 0.5083832 -0.53782152 5.907003e-01
# D_cohort_1998 0.288755900 0.1335080 2.16283663 3.055375e-02
# D_cohort_1999 0.163424236 0.1362610 1.19934721 2.303930e-01
# D_cohort_2000 -0.264981486 0.1398301 -1.89502518 5.808907e-02
# D_cohort_2001 0.149829430 0.1438733 1.04139815 2.976908e-01
# D_cohort_2002 -0.374386828 0.1483681 -2.52336417 1.162380e-02
# D_cohort_2003 -0.198735893 0.1533567 -1.29590632 1.950078e-01
# D_cohort_2004 -0.008807130 0.1589136 -0.05542087 9.558032e-01
# D_cohort_2005 -0.005337953 0.1651428 -0.03232325 9.742143e-01
# D_cohort_2006 -0.132272851 0.1721838 -0.76820710 4.423642e-01
# D_cohort_2007 -0.021862643 0.1802245 -0.12130783 9.034472e-01
# D_cohort_2008 -0.472602270 0.1895226 -2.49364600 1.264386e-02
# D_cohort_2009 -0.437572798 0.2004421 -2.18303804 2.903301e-02
# D_cohort_2010 0.295511564 0.2135164 1.38402260 1.663515e-01
# D_cohort_2011 0.310545832 0.2295651 1.35275725 1.761332e-01
# D_cohort_2012 -0.268692406 0.2499291 -1.07507473 2.823413e-01
# D_cohort_2013 0.142131410 0.2769988 0.51311192 6.078730e-01
# D_cohort_2014 0.201777590 0.3156054 0.63933494 5.226051e-01
# D_cohort_2015 -0.092672697 0.3777268 -0.24534320 8.061907e-01
# D_cohort_2016 0.872997251 0.5083832 1.71720334 8.594203e-02
# > fit.ac$s2
# [1] 0.1693316
# > fit.ac$RSS
# [1] 28.9557
# > fit.ac$RSS
forecast <- apc.forecast.ac(fit.ac,quantiles=c(0.995))
forecast$response.forecast.coh
#########################
# > forecast$response.forecast.coh
# forecast se se.proc se.est t-0.995
# coh_2 1871.073 1026.463 707.4405 743.7428 4544.891
# coh_3 5099.330 1874.681 1375.8435 1273.3744 9982.659
# coh_4 7171.317 2123.128 1622.5220 1369.3412 12701.822
# coh_5 11699.350 2984.949 2274.8292 1932.6338 19474.801
# coh_6 13717.388 3345.138 2654.4080 2035.6984 22431.090
# coh_7 14343.522 3188.410 2471.3130 2014.5886 22648.964
# coh_8 18377.001 3834.057 2910.9751 2495.2390 28364.281
# coh_9 25488.052 5241.618 3976.5389 3414.9225 39141.867
# coh_10 30524.942 6213.652 4662.3320 4107.5694 46710.794
# coh_11 40078.245 8115.990 5976.5789 5490.8835 61219.471
# coh_12 32680.319 6603.511 4727.4210 4610.6241 49881.712
# coh_13 28509.077 5895.265 4143.1332 4193.8760 43865.568
# coh_14 51760.526 11013.030 7540.3989 8026.7807 80448.208
# coh_15 98747.731 22063.641 14798.3216 16365.0210 156220.991
# coh_16 100330.677 23254.845 14704.7084 18015.5316 160906.889
# coh_17 149813.314 36629.836 21310.2885 29792.8931 245229.846
# coh_18 221549.649 58610.037 29815.3239 50459.7158 374222.093
# coh_19 229480.904 69931.745 29102.9866 63588.2473 411645.102
# coh_20 575343.178 235016.967 70362.1087 224236.8135 1187535.497
|
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