Nothing
inst/unitTests/runit.quantile.MackChainLadder.R
In ChainLadder: Statistical Methods and Models for Claims Reserving in General Insurance
test.Mack1993 <- function() {
## by Eric Dal Moro
## Check the additional Skewness elements addedto MachChainLadder function on the Mack 1993 triangles
## Results are in the paper by Eric Dal Moro:
## "An approximation of the non-life reserve risk distribution using the Cornish-Fisher expansion"
## available at SSRN: https://ssrn.com/abstract=2965384
Test <- MackChainLadder(GenIns, est.sigma="Mack")
q <- quantile(Test,0.65)
## Table 1 in the above paper
Skewness <- c(0, 0, -0.029, -0.043, -0.001, 0.180, 0.055, 0.267, 0.286, 0.314)
OverSkew <- 0.214
## test output from MackChainLadder
checkEquals(q$ByOrigin$Skewness, Skewness,tol=0.0015, checkNames = FALSE)
checkEquals(q$Totals$Totals[1], OverSkew,tol=0.0015, checkNames = FALSE)
}
test.SCORLiabProp <- function() {
## by Eric Dal Moro
## Check the additional Skewness elements addedto MachChainLadder function on the Mack 1993 triangles
## Results are in the paper by Eric Dal Moro:
## "An approximation of the non-life reserve risk distribution using the Cornish-Fisher expansion"
## available at SSRN: https://ssrn.com/abstract=2965384
SCORLiabProp <- structure(
list(V1 = c(1235909L, 1377332L, 2227264L, 6063523L,
17046209L, 19133946L, 15294531L, 18460498L, 23542477L, 17341979L,
19850416L, 16449001L, 27153648L, 30745977L, 14911754L), V2 = c(28084788L,
35709204L, 38477741L, 77188565L, 118335598L, 129368180L, 146782533L,
117030644L, 113067832L, 122713595L, 134682628L, 125616958L, 144171990L,
141700503L, NA), V3 = c(36277376L, 43213075L, 50151725L, 106217291L,
149317461L, 158428296L, 181032613L, 146526379L, 125103424L, 142017246L,
163649787L, 155143936L, 164553451L, NA, NA), V4 = c(40475255L,
51753287L, 53966008L, 113964643L, 158231476L, 161509739L, 182220943L,
132681719L, 143385679L, 154409430L, 168464316L, 158477086L, NA,
NA, NA), V5 = c(43219640L, 56669470L, 54671130L, 120412934L,
169819782L, 164007156L, 171358201L, 130134713L, 143172588L, 144452872L,
170525178L, NA, NA, NA, NA), V6 = c(44663902L, 57444929L, 57692644L,
126472874L, 171982468L, 161788099L, 171997288L, 124721542L, 130016839L,
134267844L, NA, NA, NA, NA, NA), V7 = c(45326054L, 59800911L,
60487201L, 124422859L, 171861629L, 163095804L, 170664146L, 133009259L,
125328953L, NA, NA, NA, NA, NA, NA), V8 = c(48497970L, 61566321L,
61814232L, 128806243L, 180041898L, 160465113L, 171561713L, 136533267L,
NA, NA, NA, NA, NA, NA, NA), V9 = c(49233469L, 62121477L, 61750678L,
127982137L, 178223074L, 165298176L, 169645162L, NA, NA, NA, NA,
NA, NA, NA, NA), V10 = c(49550622L, 62876588L, 62642901L, 125512850L,
178218074L, 166467315L, NA, NA, NA, NA, NA, NA, NA, NA, NA),
V11 = structure(c(4L, 6L, 5L, 2L, 3L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L), .Label = c("", "134339552", "180474109",
"49690989.5", "62622432", "62731073"), class = "factor"),
V12 = c(49831357L, 63128635L, 61843626L, 135190968L, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA), V13 = c(50360419L,
63478522L, 62208577L, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA), V14 = c(49973713L, 63123300L, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA), V15 = c(49862952L, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA)), class = "data.frame", row.names = c(NA,
-15L))
Test <- MackChainLadder(SCORLiabProp, est.sigma="Mack")
q<-quantile(Test,0.65)
## Table 1 in the above paper
Skewness <- c(0, 0, -0.032, 0.157, -0.416, 0.542, 0.418, 0.392, 0.203, 0.226, 0.036, 0.048, 0.015, 0.060, 0.925)
OverSkew <- 0.534
## test output from MackChainLadder
checkEquals(q$ByOrigin$Skewness, Skewness,tol=0.0015, checkNames = FALSE)
checkEquals(q$Totals$Totals[1], OverSkew,tol=0.0015, checkNames = FALSE)
}
test.SCORMotorNP <- function() {
## by Eric Dal Moro
## Check the additional Skewness elements addedto MachChainLadder function on the Mack 1993 triangles
## Results are in the paper by Eric Dal Moro:
## "An approximation of the non-life reserve risk distribution using the Cornish-Fisher expansion"
## available at SSRN: https://ssrn.com/abstract=2965384
SCORMotorNP <- structure(list(V1 = c(10423937L, 19822329L, 16289990L, 17124281L,
20515740L, 33482519L, 27392045L, 19607049L, 14194503L, 19089137L,
22663556L, 24538834L, 19272742L, 14389656L, 17306007L), V2 = c(38199157L,
62295888L, 85826755L, 57203907L, 74875340L, 92014269L, 96643323L,
61499050L, 36060482L, 53803738L, 54418824L, 71839634L, 54901732L,
45362116L, NA), V3 = c(56447001L, 67897838L, 104560866L, 88346499L,
112483709L, 129305456L, 123004812L, 81282483L, 42749759L, 66496545L,
73046329L, 88048826L, 68136199L, NA, NA), V4 = c(65220946L, 78668550L,
121691315L, 109965887L, 132861474L, 150572754L, 144947690L, 88308523L,
48177878L, 76630418L, 82194820L, 99525306L, NA, NA, NA), V5 = c(69971047L,
87437467L, 142404493L, 118628540L, 155637649L, 163499855L, 145787570L,
91759024L, 56986475L, 87210128L, 89086080L, NA, NA, NA, NA),
V6 = c(75438044L, 101244678L, 148725556L, 126194567L, 169622852L,
165457892L, 148529812L, 92962986L, 61193539L, 93216641L,
NA, NA, NA, NA, NA), V7 = c(82032154L, 105098260L, 153628342L,
135670962L, 178165835L, 172624920L, 151376613L, 92866952L,
61669910L, NA, NA, NA, NA, NA, NA), V8 = c(88917308L, 106590001L,
160474637L, 137597240L, 184091134L, 174772280L, 153343145L,
92770919L, NA, NA, NA, NA, NA, NA, NA), V9 = c(90783545L,
113349293L, 165538675L, 139736825L, 191246803L, 182143897L,
156330256L, NA, NA, NA, NA, NA, NA, NA, NA), V10 = c(95891585L,
115150660L, 169936112L, 139880019L, 195323123L, 184582942L,
NA, NA, NA, NA, NA, NA, NA, NA, NA), V11 = c(96943325L, 117761459L,
173201144L, 142610492L, 203866747L, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA), V12 = c(99646098L, 119647411L, 176369649L,
145133035L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA),
V13 = c(104075520L, 125137281L, 177284240L, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA), V14 = c(105688533L, 128007498L,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA), V15 = c(107081042L,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA)), class = "data.frame", row.names = c(NA,
-15L))
Test <- MackChainLadder(SCORMotorNP, est.sigma="Mack")
q<-quantile(Test,0.65)
## Table 1 in the above paper
Skewness <- c(0, 0, -0.037, -0.138, -0.115, -0.026, 0.059, 0.101, 0.236, 0.185, 0.271, 0.142, 0.174, 0.278, 1.001)
OverSkew <- 0.333
## test output from MackChainLadder
checkEquals(q$ByOrigin$Skewness, Skewness,tol=0.0015, checkNames = FALSE)
checkEquals(q$Totals$Totals[1], OverSkew,tol=0.0015, checkNames = FALSE)
}
test.EverestLiabProp <- function() {
## by Eric Dal Moro
## Check the additional Skewness elements addedto MachChainLadder function on the Mack 1993 triangles
## Results are in the paper by Eric Dal Moro:
## "An approximation of the non-life reserve risk distribution using the Cornish-Fisher expansion"
## available at SSRN: https://ssrn.com/abstract=2965384
EverestLiabProp <-
structure(list(V1 = structure(c(14L, 12L, 7L, 5L, 8L, 13L, 6L,
4L, 11L, 1L, 15L, 2L, 3L, 9L, 10L), .Label = c("10246.43364",
"11966.76086", "12389.8289", "14989.26158", "15034.82007", "17052.61259",
"19800.40144", "22740.82325", "23208.95429", "23597.23168", "26036.49293",
"30331.90775", "30487.559", "36876.5904", "9095.21897"), class = "factor"),
V2 = structure(c(4L, 5L, 13L, 8L, 2L, 6L, 3L, 12L, 15L, 11L,
14L, 7L, 10L, 9L, 1L), .Label = c("", "106402.1415", "112551.2839",
"140848.3857", "157220.7398", "179295.6903", "75167.85228",
"77036.98736", "80971.43469", "81222.54378", "82892.07045",
"86528.25398", "87915.79907", "91460.21805", "96951.10339"
), class = "factor"), V3 = structure(c(11L, 13L, 5L, 2L,
7L, 14L, 10L, 9L, 8L, 6L, 12L, 4L, 3L, 1L, 1L), .Label = c("",
"110772.902", "157514.838", "163572.4168", "173819.4772",
"179779.8443", "183879.5461", "184718.5317", "189239.0202",
"190082.4979", "196020.3914", "200206.9786", "231052.1068",
"266713.4487"), class = "factor"), V4 = structure(c(3L, 10L,
7L, 2L, 5L, 13L, 8L, 6L, 9L, 11L, 12L, 4L, 1L, 1L, 1L), .Label = c("",
"141775.4169", "217210.7681", "228819.5142", "231279.1431",
"242857.9138", "247546.6685", "254535.9137", "260475.7492",
"266469.9219", "275120.2921", "302001.2452", "322505.5772"
), class = "factor"), V5 = structure(c(3L, 8L, 5L, 2L, 4L,
12L, 6L, 7L, 9L, 11L, 10L, 1L, 1L, 1L, 1L), .Label = c("",
"162717.2621", "241180.0026", "270510.6505", "287608.1862",
"292175.5239", "302521.43", "307192.5355", "314292.0504",
"345288.0338", "345622.7611", "358495.8164"), class = "factor"),
V6 = structure(c(3L, 7L, 6L, 2L, 4L, 11L, 5L, 8L, 9L, 10L,
1L, 1L, 1L, 1L, 1L), .Label = c("", "170209.8253", "260293.4868",
"289426.7806", "309153.7089", "318432.9035", "330973.5113",
"336121.9976", "370283.8048", "385155.3338", "388816.7237"
), class = "factor"), V7 = structure(c(3L, 8L, 6L, 2L, 4L,
10L, 5L, 7L, 9L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"175176.8713", "269774.398", "298728.9968", "347308.4394",
"353917.4185", "355555.9263", "366930.7128", "373355.5652",
"400856.4437"), class = "factor"), V8 = structure(c(3L, 8L,
7L, 2L, 4L, 9L, 5L, 6L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"181045.1928", "280547.3895", "317636.005", "350355.6888",
"362170.5627", "365497.5958", "397231.3802", "409483.8956"
), class = "factor"), V9 = structure(c(3L, 7L, 6L, 2L, 4L,
8L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("", "188111.0313",
"285868.2907", "318600.5707", "352107.614", "373239.2429",
"400229.8033", "414233.5787"), class = "factor"), V10 = structure(c(3L,
6L, 5L, 2L, 4L, 7L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"189062.0699", "285422.4511", "319543.6974", "371967.3318",
"401874.2856", "421622.0302"), class = "factor"), V11 = structure(c(3L,
6L, 5L, 2L, 4L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"192628.1888", "287229.4003", "321864.6556", "357969.3852",
"402541.3146"), class = "factor"), V12 = structure(c(3L,
5L, 4L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"193112.6453", "288844.1791", "362053.5247", "406851.5549"
), class = "factor"), V13 = structure(c(2L, 4L, 3L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("", "292834.6376",
"362610.3615", "407249.6905"), class = "factor"), V14 = structure(c(2L,
3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"293091.3643", "401579.9039"), class = "factor"), V15 = structure(c(2L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"293894.6895"), class = "factor")), class = "data.frame", row.names = c(NA,
-15L))
Test <- MackChainLadder(EverestLiabProp, est.sigma="Mack")
q<-quantile(Test,0.65)
## Table 1 in the above paper
Skewness <- c(0, 0, 0.042, 0.087, 0.065, -0.268, -0.234, -0.164, 0.075, 0.157, 0.245, 0.289, 0.168, 0.231, 0.547)
OverSkew <- 0.321
## test output from MackChainLadder
checkEquals(q$ByOrigin$Skewness, Skewness,tol=0.0015, checkNames = FALSE)
checkEquals(q$Totals$Totals[1], OverSkew,tol=0.0015, checkNames = FALSE)
}
test.EverestLiabNP <- function() {
## by Eric Dal Moro
## Check the additional Skewness elements addedto MachChainLadder function on the Mack 1993 triangles
## Results are in the paper by Eric Dal Moro:
## "An approximation of the non-life reserve risk distribution using the Cornish-Fisher expansion"
## available at SSRN: https://ssrn.com/abstract=2965384
EverestLiabNP <-
structure(list(V1 = structure(c(12L, 5L, 1L, 9L, 3L, 11L, 14L,
2L, 15L, 13L, 8L, 4L, 10L, 6L, 7L), .Label = c("13487.22446",
"13601.21197", "14156.05241", "15008.1105", "16277.70345", "17061.02818",
"17290.72214", "18237.28932", "20508.30826", "21591.94393", "30721.08172",
"46760.60193", "7085.357535", "7305.207426", "9656.973343"), class = "factor"),
V2 = structure(c(2L, 15L, 11L, 14L, 12L, 13L, 3L, 7L, 5L,
4L, 9L, 8L, 10L, 6L, 1L), .Label = c("", "111719.3417", "38247.68233",
"48158.19048", "48466.35934", "50129.18197", "54170.45943",
"56672.38118", "57128.59988", "62379.84002", "64108.57119",
"64518.4658", "71996.15154", "76554.87292", "98774.76192"
), class = "factor"), V3 = structure(c(8L, 7L, 5L, 6L, 4L,
12L, 9L, 10L, 13L, 2L, 3L, 14L, 11L, 1L, 1L), .Label = c("",
"103903.4474", "108752.239", "118329.7139", "137044.5158",
"158876.1332", "199365.1559", "200320.1304", "67827.27694",
"76370.26183", "88974.99053", "91632.6811", "96303.45733",
"96719.5756"), class = "factor"), V4 = structure(c(11L, 10L,
9L, 8L, 7L, 2L, 12L, 13L, 4L, 6L, 5L, 3L, 1L, 1L, 1L), .Label = c("",
"122357.4179", "122553.9778", "128290.0558", "148642.6167",
"149927.1491", "161614.475", "205166.6118", "225561.7252",
"300592.385", "307924.4259", "92922.00769", "96750.2668"), class = "factor"),
V5 = structure(c(12L, 11L, 10L, 9L, 8L, 5L, 2L, 3L, 4L, 6L,
7L, 1L, 1L, 1L, 1L), .Label = c("", "110462.8506", "117890.6472",
"150367.2558", "151180.1638", "167151.7234", "177825.2832",
"190324.306", "289669.705", "294301.0502", "386756.2697",
"390393.5155"), class = "factor"), V6 = structure(c(10L,
11L, 9L, 8L, 7L, 5L, 2L, 3L, 4L, 6L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"119865.282", "128013.3674", "156742.0401", "172285.9609",
"186972.1784", "222191.2372", "341325.6987", "348384.9662",
"447214.7594", "450659.4391"), class = "factor"), V7 = structure(c(9L,
10L, 7L, 8L, 6L, 5L, 3L, 2L, 4L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"127441.7619", "128818.542", "164004.4024", "176968.5872",
"253620.8479", "381020.7083", "396566.8562", "478440.6414",
"503910.8058"), class = "factor"), V8 = structure(c(8L, 9L,
6L, 7L, 5L, 4L, 3L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"133228.798", "133455.1831", "185704.0347", "271621.4606",
"396413.1669", "412016.2346", "496763.0668", "532179.1653"
), class = "factor"), V9 = structure(c(7L, 8L, 5L, 6L, 4L,
3L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("", "140558.7505",
"183775.9392", "284278.1226", "409978.4846", "426038.9289",
"515705.6548", "559183.434"), class = "factor"), V10 = structure(c(6L,
7L, 4L, 5L, 3L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"186713.7108", "290607.9122", "415996.405", "437417.0563",
"528866.4506", "598937.7059"), class = "factor"), V11 = structure(c(5L,
6L, 3L, 4L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"295659.6674", "417044.4002", "455037.9521", "537367.3064",
"629929.7835"), class = "factor"), V12 = structure(c(4L,
5L, 2L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"421067.7427", "461282.2011", "546360.2662", "643214.2754"
), class = "factor"), V13 = structure(c(3L, 4L, 2L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("", "425868.262",
"554378.5544", "655053.977"), class = "factor"), V14 = structure(c(2L,
3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"558865.8598", "666091.3122"), class = "factor"), V15 = structure(c(2L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"559492.5341"), class = "factor")), class = "data.frame", row.names = c(NA,
-15L))
Test <- MackChainLadder(EverestLiabNP, est.sigma="Mack")
q<-quantile(Test,0.65)
## Table 1 in the above paper
Skewness <- c(0, 0, -0.024, -0.016, -0.008, 0.100, 0.399, 0.241, 0.229, 0.129, 0.034, 0.224, 0.340, 0.017, 0.485)
OverSkew <- 0.318
## test output from MackChainLadder
checkEquals(q$ByOrigin$Skewness, Skewness,tol=0.0015, checkNames = FALSE)
checkEquals(q$Totals$Totals[1], OverSkew,tol=0.0015, checkNames = FALSE)
}
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test.Mack1993 <- function() {
## by Eric Dal Moro
## Check the additional Skewness elements addedto MachChainLadder function on the Mack 1993 triangles
## Results are in the paper by Eric Dal Moro:
## "An approximation of the non-life reserve risk distribution using the Cornish-Fisher expansion"
## available at SSRN: https://ssrn.com/abstract=2965384
Test <- MackChainLadder(GenIns, est.sigma="Mack")
q <- quantile(Test,0.65)
## Table 1 in the above paper
Skewness <- c(0, 0, -0.029, -0.043, -0.001, 0.180, 0.055, 0.267, 0.286, 0.314)
OverSkew <- 0.214
## test output from MackChainLadder
checkEquals(q$ByOrigin$Skewness, Skewness,tol=0.0015, checkNames = FALSE)
checkEquals(q$Totals$Totals[1], OverSkew,tol=0.0015, checkNames = FALSE)
}
test.SCORLiabProp <- function() {
## by Eric Dal Moro
## Check the additional Skewness elements addedto MachChainLadder function on the Mack 1993 triangles
## Results are in the paper by Eric Dal Moro:
## "An approximation of the non-life reserve risk distribution using the Cornish-Fisher expansion"
## available at SSRN: https://ssrn.com/abstract=2965384
SCORLiabProp <- structure(
list(V1 = c(1235909L, 1377332L, 2227264L, 6063523L,
17046209L, 19133946L, 15294531L, 18460498L, 23542477L, 17341979L,
19850416L, 16449001L, 27153648L, 30745977L, 14911754L), V2 = c(28084788L,
35709204L, 38477741L, 77188565L, 118335598L, 129368180L, 146782533L,
117030644L, 113067832L, 122713595L, 134682628L, 125616958L, 144171990L,
141700503L, NA), V3 = c(36277376L, 43213075L, 50151725L, 106217291L,
149317461L, 158428296L, 181032613L, 146526379L, 125103424L, 142017246L,
163649787L, 155143936L, 164553451L, NA, NA), V4 = c(40475255L,
51753287L, 53966008L, 113964643L, 158231476L, 161509739L, 182220943L,
132681719L, 143385679L, 154409430L, 168464316L, 158477086L, NA,
NA, NA), V5 = c(43219640L, 56669470L, 54671130L, 120412934L,
169819782L, 164007156L, 171358201L, 130134713L, 143172588L, 144452872L,
170525178L, NA, NA, NA, NA), V6 = c(44663902L, 57444929L, 57692644L,
126472874L, 171982468L, 161788099L, 171997288L, 124721542L, 130016839L,
134267844L, NA, NA, NA, NA, NA), V7 = c(45326054L, 59800911L,
60487201L, 124422859L, 171861629L, 163095804L, 170664146L, 133009259L,
125328953L, NA, NA, NA, NA, NA, NA), V8 = c(48497970L, 61566321L,
61814232L, 128806243L, 180041898L, 160465113L, 171561713L, 136533267L,
NA, NA, NA, NA, NA, NA, NA), V9 = c(49233469L, 62121477L, 61750678L,
127982137L, 178223074L, 165298176L, 169645162L, NA, NA, NA, NA,
NA, NA, NA, NA), V10 = c(49550622L, 62876588L, 62642901L, 125512850L,
178218074L, 166467315L, NA, NA, NA, NA, NA, NA, NA, NA, NA),
V11 = structure(c(4L, 6L, 5L, 2L, 3L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L), .Label = c("", "134339552", "180474109",
"49690989.5", "62622432", "62731073"), class = "factor"),
V12 = c(49831357L, 63128635L, 61843626L, 135190968L, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA), V13 = c(50360419L,
63478522L, 62208577L, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA), V14 = c(49973713L, 63123300L, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA), V15 = c(49862952L, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA)), class = "data.frame", row.names = c(NA,
-15L))
Test <- MackChainLadder(SCORLiabProp, est.sigma="Mack")
q<-quantile(Test,0.65)
## Table 1 in the above paper
Skewness <- c(0, 0, -0.032, 0.157, -0.416, 0.542, 0.418, 0.392, 0.203, 0.226, 0.036, 0.048, 0.015, 0.060, 0.925)
OverSkew <- 0.534
## test output from MackChainLadder
checkEquals(q$ByOrigin$Skewness, Skewness,tol=0.0015, checkNames = FALSE)
checkEquals(q$Totals$Totals[1], OverSkew,tol=0.0015, checkNames = FALSE)
}
test.SCORMotorNP <- function() {
## by Eric Dal Moro
## Check the additional Skewness elements addedto MachChainLadder function on the Mack 1993 triangles
## Results are in the paper by Eric Dal Moro:
## "An approximation of the non-life reserve risk distribution using the Cornish-Fisher expansion"
## available at SSRN: https://ssrn.com/abstract=2965384
SCORMotorNP <- structure(list(V1 = c(10423937L, 19822329L, 16289990L, 17124281L,
20515740L, 33482519L, 27392045L, 19607049L, 14194503L, 19089137L,
22663556L, 24538834L, 19272742L, 14389656L, 17306007L), V2 = c(38199157L,
62295888L, 85826755L, 57203907L, 74875340L, 92014269L, 96643323L,
61499050L, 36060482L, 53803738L, 54418824L, 71839634L, 54901732L,
45362116L, NA), V3 = c(56447001L, 67897838L, 104560866L, 88346499L,
112483709L, 129305456L, 123004812L, 81282483L, 42749759L, 66496545L,
73046329L, 88048826L, 68136199L, NA, NA), V4 = c(65220946L, 78668550L,
121691315L, 109965887L, 132861474L, 150572754L, 144947690L, 88308523L,
48177878L, 76630418L, 82194820L, 99525306L, NA, NA, NA), V5 = c(69971047L,
87437467L, 142404493L, 118628540L, 155637649L, 163499855L, 145787570L,
91759024L, 56986475L, 87210128L, 89086080L, NA, NA, NA, NA),
V6 = c(75438044L, 101244678L, 148725556L, 126194567L, 169622852L,
165457892L, 148529812L, 92962986L, 61193539L, 93216641L,
NA, NA, NA, NA, NA), V7 = c(82032154L, 105098260L, 153628342L,
135670962L, 178165835L, 172624920L, 151376613L, 92866952L,
61669910L, NA, NA, NA, NA, NA, NA), V8 = c(88917308L, 106590001L,
160474637L, 137597240L, 184091134L, 174772280L, 153343145L,
92770919L, NA, NA, NA, NA, NA, NA, NA), V9 = c(90783545L,
113349293L, 165538675L, 139736825L, 191246803L, 182143897L,
156330256L, NA, NA, NA, NA, NA, NA, NA, NA), V10 = c(95891585L,
115150660L, 169936112L, 139880019L, 195323123L, 184582942L,
NA, NA, NA, NA, NA, NA, NA, NA, NA), V11 = c(96943325L, 117761459L,
173201144L, 142610492L, 203866747L, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA), V12 = c(99646098L, 119647411L, 176369649L,
145133035L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA),
V13 = c(104075520L, 125137281L, 177284240L, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA), V14 = c(105688533L, 128007498L,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA), V15 = c(107081042L,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA)), class = "data.frame", row.names = c(NA,
-15L))
Test <- MackChainLadder(SCORMotorNP, est.sigma="Mack")
q<-quantile(Test,0.65)
## Table 1 in the above paper
Skewness <- c(0, 0, -0.037, -0.138, -0.115, -0.026, 0.059, 0.101, 0.236, 0.185, 0.271, 0.142, 0.174, 0.278, 1.001)
OverSkew <- 0.333
## test output from MackChainLadder
checkEquals(q$ByOrigin$Skewness, Skewness,tol=0.0015, checkNames = FALSE)
checkEquals(q$Totals$Totals[1], OverSkew,tol=0.0015, checkNames = FALSE)
}
test.EverestLiabProp <- function() {
## by Eric Dal Moro
## Check the additional Skewness elements addedto MachChainLadder function on the Mack 1993 triangles
## Results are in the paper by Eric Dal Moro:
## "An approximation of the non-life reserve risk distribution using the Cornish-Fisher expansion"
## available at SSRN: https://ssrn.com/abstract=2965384
EverestLiabProp <-
structure(list(V1 = structure(c(14L, 12L, 7L, 5L, 8L, 13L, 6L,
4L, 11L, 1L, 15L, 2L, 3L, 9L, 10L), .Label = c("10246.43364",
"11966.76086", "12389.8289", "14989.26158", "15034.82007", "17052.61259",
"19800.40144", "22740.82325", "23208.95429", "23597.23168", "26036.49293",
"30331.90775", "30487.559", "36876.5904", "9095.21897"), class = "factor"),
V2 = structure(c(4L, 5L, 13L, 8L, 2L, 6L, 3L, 12L, 15L, 11L,
14L, 7L, 10L, 9L, 1L), .Label = c("", "106402.1415", "112551.2839",
"140848.3857", "157220.7398", "179295.6903", "75167.85228",
"77036.98736", "80971.43469", "81222.54378", "82892.07045",
"86528.25398", "87915.79907", "91460.21805", "96951.10339"
), class = "factor"), V3 = structure(c(11L, 13L, 5L, 2L,
7L, 14L, 10L, 9L, 8L, 6L, 12L, 4L, 3L, 1L, 1L), .Label = c("",
"110772.902", "157514.838", "163572.4168", "173819.4772",
"179779.8443", "183879.5461", "184718.5317", "189239.0202",
"190082.4979", "196020.3914", "200206.9786", "231052.1068",
"266713.4487"), class = "factor"), V4 = structure(c(3L, 10L,
7L, 2L, 5L, 13L, 8L, 6L, 9L, 11L, 12L, 4L, 1L, 1L, 1L), .Label = c("",
"141775.4169", "217210.7681", "228819.5142", "231279.1431",
"242857.9138", "247546.6685", "254535.9137", "260475.7492",
"266469.9219", "275120.2921", "302001.2452", "322505.5772"
), class = "factor"), V5 = structure(c(3L, 8L, 5L, 2L, 4L,
12L, 6L, 7L, 9L, 11L, 10L, 1L, 1L, 1L, 1L), .Label = c("",
"162717.2621", "241180.0026", "270510.6505", "287608.1862",
"292175.5239", "302521.43", "307192.5355", "314292.0504",
"345288.0338", "345622.7611", "358495.8164"), class = "factor"),
V6 = structure(c(3L, 7L, 6L, 2L, 4L, 11L, 5L, 8L, 9L, 10L,
1L, 1L, 1L, 1L, 1L), .Label = c("", "170209.8253", "260293.4868",
"289426.7806", "309153.7089", "318432.9035", "330973.5113",
"336121.9976", "370283.8048", "385155.3338", "388816.7237"
), class = "factor"), V7 = structure(c(3L, 8L, 6L, 2L, 4L,
10L, 5L, 7L, 9L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"175176.8713", "269774.398", "298728.9968", "347308.4394",
"353917.4185", "355555.9263", "366930.7128", "373355.5652",
"400856.4437"), class = "factor"), V8 = structure(c(3L, 8L,
7L, 2L, 4L, 9L, 5L, 6L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"181045.1928", "280547.3895", "317636.005", "350355.6888",
"362170.5627", "365497.5958", "397231.3802", "409483.8956"
), class = "factor"), V9 = structure(c(3L, 7L, 6L, 2L, 4L,
8L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("", "188111.0313",
"285868.2907", "318600.5707", "352107.614", "373239.2429",
"400229.8033", "414233.5787"), class = "factor"), V10 = structure(c(3L,
6L, 5L, 2L, 4L, 7L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"189062.0699", "285422.4511", "319543.6974", "371967.3318",
"401874.2856", "421622.0302"), class = "factor"), V11 = structure(c(3L,
6L, 5L, 2L, 4L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"192628.1888", "287229.4003", "321864.6556", "357969.3852",
"402541.3146"), class = "factor"), V12 = structure(c(3L,
5L, 4L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"193112.6453", "288844.1791", "362053.5247", "406851.5549"
), class = "factor"), V13 = structure(c(2L, 4L, 3L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("", "292834.6376",
"362610.3615", "407249.6905"), class = "factor"), V14 = structure(c(2L,
3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"293091.3643", "401579.9039"), class = "factor"), V15 = structure(c(2L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"293894.6895"), class = "factor")), class = "data.frame", row.names = c(NA,
-15L))
Test <- MackChainLadder(EverestLiabProp, est.sigma="Mack")
q<-quantile(Test,0.65)
## Table 1 in the above paper
Skewness <- c(0, 0, 0.042, 0.087, 0.065, -0.268, -0.234, -0.164, 0.075, 0.157, 0.245, 0.289, 0.168, 0.231, 0.547)
OverSkew <- 0.321
## test output from MackChainLadder
checkEquals(q$ByOrigin$Skewness, Skewness,tol=0.0015, checkNames = FALSE)
checkEquals(q$Totals$Totals[1], OverSkew,tol=0.0015, checkNames = FALSE)
}
test.EverestLiabNP <- function() {
## by Eric Dal Moro
## Check the additional Skewness elements addedto MachChainLadder function on the Mack 1993 triangles
## Results are in the paper by Eric Dal Moro:
## "An approximation of the non-life reserve risk distribution using the Cornish-Fisher expansion"
## available at SSRN: https://ssrn.com/abstract=2965384
EverestLiabNP <-
structure(list(V1 = structure(c(12L, 5L, 1L, 9L, 3L, 11L, 14L,
2L, 15L, 13L, 8L, 4L, 10L, 6L, 7L), .Label = c("13487.22446",
"13601.21197", "14156.05241", "15008.1105", "16277.70345", "17061.02818",
"17290.72214", "18237.28932", "20508.30826", "21591.94393", "30721.08172",
"46760.60193", "7085.357535", "7305.207426", "9656.973343"), class = "factor"),
V2 = structure(c(2L, 15L, 11L, 14L, 12L, 13L, 3L, 7L, 5L,
4L, 9L, 8L, 10L, 6L, 1L), .Label = c("", "111719.3417", "38247.68233",
"48158.19048", "48466.35934", "50129.18197", "54170.45943",
"56672.38118", "57128.59988", "62379.84002", "64108.57119",
"64518.4658", "71996.15154", "76554.87292", "98774.76192"
), class = "factor"), V3 = structure(c(8L, 7L, 5L, 6L, 4L,
12L, 9L, 10L, 13L, 2L, 3L, 14L, 11L, 1L, 1L), .Label = c("",
"103903.4474", "108752.239", "118329.7139", "137044.5158",
"158876.1332", "199365.1559", "200320.1304", "67827.27694",
"76370.26183", "88974.99053", "91632.6811", "96303.45733",
"96719.5756"), class = "factor"), V4 = structure(c(11L, 10L,
9L, 8L, 7L, 2L, 12L, 13L, 4L, 6L, 5L, 3L, 1L, 1L, 1L), .Label = c("",
"122357.4179", "122553.9778", "128290.0558", "148642.6167",
"149927.1491", "161614.475", "205166.6118", "225561.7252",
"300592.385", "307924.4259", "92922.00769", "96750.2668"), class = "factor"),
V5 = structure(c(12L, 11L, 10L, 9L, 8L, 5L, 2L, 3L, 4L, 6L,
7L, 1L, 1L, 1L, 1L), .Label = c("", "110462.8506", "117890.6472",
"150367.2558", "151180.1638", "167151.7234", "177825.2832",
"190324.306", "289669.705", "294301.0502", "386756.2697",
"390393.5155"), class = "factor"), V6 = structure(c(10L,
11L, 9L, 8L, 7L, 5L, 2L, 3L, 4L, 6L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"119865.282", "128013.3674", "156742.0401", "172285.9609",
"186972.1784", "222191.2372", "341325.6987", "348384.9662",
"447214.7594", "450659.4391"), class = "factor"), V7 = structure(c(9L,
10L, 7L, 8L, 6L, 5L, 3L, 2L, 4L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"127441.7619", "128818.542", "164004.4024", "176968.5872",
"253620.8479", "381020.7083", "396566.8562", "478440.6414",
"503910.8058"), class = "factor"), V8 = structure(c(8L, 9L,
6L, 7L, 5L, 4L, 3L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"133228.798", "133455.1831", "185704.0347", "271621.4606",
"396413.1669", "412016.2346", "496763.0668", "532179.1653"
), class = "factor"), V9 = structure(c(7L, 8L, 5L, 6L, 4L,
3L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("", "140558.7505",
"183775.9392", "284278.1226", "409978.4846", "426038.9289",
"515705.6548", "559183.434"), class = "factor"), V10 = structure(c(6L,
7L, 4L, 5L, 3L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"186713.7108", "290607.9122", "415996.405", "437417.0563",
"528866.4506", "598937.7059"), class = "factor"), V11 = structure(c(5L,
6L, 3L, 4L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"295659.6674", "417044.4002", "455037.9521", "537367.3064",
"629929.7835"), class = "factor"), V12 = structure(c(4L,
5L, 2L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"421067.7427", "461282.2011", "546360.2662", "643214.2754"
), class = "factor"), V13 = structure(c(3L, 4L, 2L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("", "425868.262",
"554378.5544", "655053.977"), class = "factor"), V14 = structure(c(2L,
3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"558865.8598", "666091.3122"), class = "factor"), V15 = structure(c(2L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("",
"559492.5341"), class = "factor")), class = "data.frame", row.names = c(NA,
-15L))
Test <- MackChainLadder(EverestLiabNP, est.sigma="Mack")
q<-quantile(Test,0.65)
## Table 1 in the above paper
Skewness <- c(0, 0, -0.024, -0.016, -0.008, 0.100, 0.399, 0.241, 0.229, 0.129, 0.034, 0.224, 0.340, 0.017, 0.485)
OverSkew <- 0.318
## test output from MackChainLadder
checkEquals(q$ByOrigin$Skewness, Skewness,tol=0.0015, checkNames = FALSE)
checkEquals(q$Totals$Totals[1], OverSkew,tol=0.0015, checkNames = FALSE)
}
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