Generic functions for triangles — triangle S3 Methods • ChainLadder

Functions to ease the work with triangle shaped matrix data. A 'triangle' is a matrix with some generic functions.

triangle creates a triangle from the given set of vectors of observed data.

as.triangle attempts to turn its argument into a triangle. Triangles are usually stored in a “long” format in data bases. The function can transform a data.frame into a triangle shape.

as.data.frame turns a triangle into a data frame.

Usage

triangle(..., bycol=FALSE, origin="origin", dev="dev", value="value")

# S3 method for class 'matrix'
as.triangle(Triangle, origin="origin", dev="dev", value="value", ...)
# S3 method for class 'data.frame'
as.triangle(Triangle, origin="origin", dev="dev", value="value", ...)
# S3 method for class 'triangle'
as.data.frame(x, row.names=NULL, optional, lob=NULL, na.rm=FALSE, ...)
as.triangle(Triangle, origin="origin", dev="dev", value="value", ...)
# S3 method for class 'triangle'
plot(x, type = "b", xlab = "dev. period", ylab = NULL, lattice=FALSE, ...)

Arguments

Triangle: a triangle
bycol: logical. If FALSE (the default) the triangle is filled by rows, otherwise the triangle is filled by columns.
origin: name of the origin period, default is "origin".
dev: name of the development period, default is "dev".
value: name of the value, default is "value".
row.names: default is set to NULL and will merge origin and dev. period to create row names.
lob: default is NULL. The idea is to use lob (line of business) as an additional column to label a triangle in a long format, see the examples for more details.
optional: not used
na.rm: logical. Remove missing values?
x: a matrix of class 'triangle'

xlab: a label for the x axis, defaults to 'dev. period'
ylab: a label for the y axis, defaults to NULL
lattice: logical. If FALSE the function matplot is used to plot the developments of the triangle in one graph, otherwise the xyplot function of the lattice package is used, to plot developments of each origin period in a different panel.
type: type, see plot.default
...: vectors of data in triangle, see details; arguments to be passed to other methods everywhere else.

Details

Function triangle builds a triangle matrix from the vectors of known data provided in .... Normally, each of these vectors should be one shorter than the preceeding one. The length of the first vector dictates the number of development periods or origin periods (respectively when bycol is FALSE or TRUE). As a special case, the function will build an \(n \times n\) triangle from a single vector of \(n(n + 1)/2\) data points.

The names of the arguments in ... for function triangle (when there are more than one) are retained for row/column names. Similarly, the names of the elements of the first argument are used as column/row names.

Author

Markus Gesmann, Dan Murphy, Vincent Goulet

Warning

Please note that for the function as.triangle the origin and dev. period columns have to be of type numeric or a character which can be converted into numeric.

Also note that when converting from a data.frame to a matrix with as.triangle, multiple records with the same origin and dev will be aggregated.

Examples

GenIns
#>       dev
#> origin      1       2       3       4       5       6       7       8       9
#>     1  357848 1124788 1735330 2218270 2745596 3319994 3466336 3606286 3833515
#>     2  352118 1236139 2170033 3353322 3799067 4120063 4647867 4914039 5339085
#>     3  290507 1292306 2218525 3235179 3985995 4132918 4628910 4909315      NA
#>     4  310608 1418858 2195047 3757447 4029929 4381982 4588268      NA      NA
#>     5  443160 1136350 2128333 2897821 3402672 3873311      NA      NA      NA
#>     6  396132 1333217 2180715 2985752 3691712      NA      NA      NA      NA
#>     7  440832 1288463 2419861 3483130      NA      NA      NA      NA      NA
#>     8  359480 1421128 2864498      NA      NA      NA      NA      NA      NA
#>     9  376686 1363294      NA      NA      NA      NA      NA      NA      NA
#>     10 344014      NA      NA      NA      NA      NA      NA      NA      NA
#>       dev
#> origin      10
#>     1  3901463
#>     2       NA
#>     3       NA
#>     4       NA
#>     5       NA
#>     6       NA
#>     7       NA
#>     8       NA
#>     9       NA
#>     10      NA
plot(GenIns)

plot(GenIns, lattice=TRUE)



## Convert long format into triangle
## Triangles are usually stored as 'long' tables in data bases
head(GenInsLong)
#>   accyear devyear incurred claims
#> 1       1       1          357848
#> 2       2       1          352118
#> 3       3       1          290507
#> 4       4       1          310608
#> 5       5       1          443160
#> 6       6       1          396132
as.triangle(GenInsLong, origin="accyear", dev="devyear", "incurred claims")
#>        devyear
#> accyear      1       2       3       4       5       6       7       8       9
#>      1  357848 1124788 1735330 2218270 2745596 3319994 3466336 3606286 3833515
#>      2  352118 1236139 2170033 3353322 3799067 4120063 4647867 4914039 5339085
#>      3  290507 1292306 2218525 3235179 3985995 4132918 4628910 4909315      NA
#>      4  310608 1418858 2195047 3757447 4029929 4381982 4588268      NA      NA
#>      5  443160 1136350 2128333 2897821 3402672 3873311      NA      NA      NA
#>      6  396132 1333217 2180715 2985752 3691712      NA      NA      NA      NA
#>      7  440832 1288463 2419861 3483130      NA      NA      NA      NA      NA
#>      8  359480 1421128 2864498      NA      NA      NA      NA      NA      NA
#>      9  376686 1363294      NA      NA      NA      NA      NA      NA      NA
#>      10 344014      NA      NA      NA      NA      NA      NA      NA      NA
#>        devyear
#> accyear      10
#>      1  3901463
#>      2       NA
#>      3       NA
#>      4       NA
#>      5       NA
#>      6       NA
#>      7       NA
#>      8       NA
#>      9       NA
#>      10      NA

X <- as.data.frame(RAA)
head(X)
#>        origin dev value
#> 1981-1   1981   1  5012
#> 1982-1   1982   1   106
#> 1983-1   1983   1  3410
#> 1984-1   1984   1  5655
#> 1985-1   1985   1  1092
#> 1986-1   1986   1  1513

Y <- as.data.frame(RAA, lob="General Liability")
head(Y)
#>        origin dev value               lob
#> 1981-1   1981   1  5012 General Liability
#> 1982-1   1982   1   106 General Liability
#> 1983-1   1983   1  3410 General Liability
#> 1984-1   1984   1  5655 General Liability
#> 1985-1   1985   1  1092 General Liability
#> 1986-1   1986   1  1513 General Liability

## Basic creation of a triangle from loss development data
triangle(c(100, 150, 175, 180, 200),
         c(110, 168, 192, 205),
         c(115, 169, 202),
         c(125, 185),
         150)
#>       dev
#> origin   1   2   3   4   5
#>      1 100 150 175 180 200
#>      2 110 168 192 205  NA
#>      3 115 169 202  NA  NA
#>      4 125 185  NA  NA  NA
#>      5 150  NA  NA  NA  NA

## Same, with named origin periods
triangle("2012" = c(100, 150, 175, 180, 200),
         "2013" = c(110, 168, 192, 205),
         "2014" = c(115, 169, 202),
         "2015" = c(125, 185),
         "2016" = 150)
#>       dev
#> origin   1   2   3   4   5
#>   2012 100 150 175 180 200
#>   2013 110 168 192 205  NA
#>   2014 115 169 202  NA  NA
#>   2015 125 185  NA  NA  NA
#>   2016 150  NA  NA  NA  NA

## Again, with also named development periods
triangle("2012" = c("12 months" = 100,
                    "24 months" = 150,
                    "36 months" = 175,
                    "48 months" = 180,
                    "60 months" = 200),
         "2013" = c(110, 168, 192, 205),
         "2014" = c(115, 169, 202),
         "2015" = c(125, 185),
         "2016" = 150)
#>       dev
#> origin 12 months 24 months 36 months 48 months 60 months
#>   2012       100       150       175       180       200
#>   2013       110       168       192       205        NA
#>   2014       115       169       202        NA        NA
#>   2015       125       185        NA        NA        NA
#>   2016       150        NA        NA        NA        NA

## Quick, simplified usage
triangle(c(100, 150, 175, 110, 168, 115))
#>       dev
#> origin   1   2   3
#>      1 100 150 175
#>      2 110 168  NA
#>      3 115  NA  NA