Calculate Age-to-Age Factors

Calculate the matrix of age-to-age factors (also called "report-to-report" factors, or "link ratios") for an object of class triangle.

Usage

ata(Triangle, NArow.rm = TRUE, colname.sep = "-",
        colname.order=c("ascending","descending"))

Arguments

Triangle: a loss "triangle". Must be a matrix.
NArow.rm: logical indicating if rows of age-to-age (ata) factors that are all NA should be removed. "All-NA" rows typically occur for the most recent origin year of a loss triangle.
colname.sep: a character indicating the separator character to place between the column names of Triangle that will be used to lable the columns of the resulting matrix of ata factors
colname.order: "ascending" indicates that the less mature age comes first in the column labels of the ata matrix

Details

ata constructs a matrix of age-to-age (ata) factors resulting from a loss "triangle" or a matrix. Simple averages and volume weighted averages are saved as "smpl" and "vwtd" attributes, respectively.

Value

A matrix with "smpl" and "vwtd" attributes.

Author

Daniel Murphy

Examples

ata(GenIns)
#>       dev
#> origin   1-2   2-3   3-4   4-5   5-6   6-7   7-8   8-9  9-10
#>   1    3.143 1.543 1.278 1.238 1.209 1.044 1.040 1.063 1.018
#>   2    3.511 1.755 1.545 1.133 1.084 1.128 1.057 1.086    NA
#>   3    4.448 1.717 1.458 1.232 1.037 1.120 1.061    NA    NA
#>   4    4.568 1.547 1.712 1.073 1.087 1.047    NA    NA    NA
#>   5    2.564 1.873 1.362 1.174 1.138    NA    NA    NA    NA
#>   6    3.366 1.636 1.369 1.236    NA    NA    NA    NA    NA
#>   7    2.923 1.878 1.439    NA    NA    NA    NA    NA    NA
#>   8    3.953 2.016    NA    NA    NA    NA    NA    NA    NA
#>   9    3.619    NA    NA    NA    NA    NA    NA    NA    NA
#>   smpl 3.566 1.746 1.452 1.181 1.111 1.085 1.053 1.075 1.018
#>   vwtd 3.491 1.747 1.457 1.174 1.104 1.086 1.054 1.077 1.018

# Volume weighted average age-to-age factor of the "RAA" data
y <- attr(ata(RAA), "vwtd")
y
#>      1-2      2-3      3-4      4-5      5-6      6-7      7-8      8-9 
#> 2.999359 1.623523 1.270888 1.171675 1.113385 1.041935 1.033264 1.016936 
#>     9-10 
#> 1.009217 
# "To ultimate" factors with a 10% tail
y <- rev(cumprod(rev(c(y, 1.1))))
names(y) <- paste(colnames(RAA), "Ult", sep="-")
y
#>    1-Ult    2-Ult    3-Ult    4-Ult    5-Ult    6-Ult    7-Ult    8-Ult 
#> 9.812257 3.271452 2.015033 1.585531 1.353218 1.215409 1.166493 1.128940 
#>    9-Ult   10-Ult 
#> 1.110138 1.100000 

## Label the development columns in "ratio-type" format
ata(RAA, colname.sep=":", colname.order="desc")
#>       dev
#> origin    2:1   3:2   4:3   5:4   6:5   7:6   8:7   9:8  10:9
#>   1981  1.650 1.319 1.082 1.147 1.195 1.113 1.033 1.003 1.009
#>   1982 40.425 1.259 1.977 1.292 1.132 0.993 1.043 1.033    NA
#>   1983  2.637 1.543 1.163 1.161 1.186 1.029 1.026    NA    NA
#>   1984  2.043 1.364 1.349 1.102 1.113 1.038    NA    NA    NA
#>   1985  8.759 1.656 1.400 1.171 1.009    NA    NA    NA    NA
#>   1986  4.260 1.816 1.105 1.226    NA    NA    NA    NA    NA
#>   1987  7.217 2.723 1.125    NA    NA    NA    NA    NA    NA
#>   1988  5.142 1.887    NA    NA    NA    NA    NA    NA    NA
#>   1989  1.722    NA    NA    NA    NA    NA    NA    NA    NA
#>   smpl  8.206 1.696 1.315 1.183 1.127 1.043 1.034 1.018 1.009
#>   vwtd  2.999 1.624 1.271 1.172 1.113 1.042 1.033 1.017 1.009