Triangles function

Generic functions for triangles

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. 1.1

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 c("$n\n$", "$\\times n$") 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(s)

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
plot(GenIns)
plot(GenIns, lattice=TRUE)

## Convert long format into triangle
## Triangles are usually stored as 'long' tables in data bases
head(GenInsLong)
as.triangle(GenInsLong, origin="accyear", dev="devyear", "incurred claims")

X <- as.data.frame(RAA)
head(X)

Y <- as.data.frame(RAA, lob="General Liability")
head(Y)

## 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)

## 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)

## 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)

## Quick, simplified usage
triangle(c(100, 150, 175, 110, 168, 115))