
Calculate Age-to-Age Factors
ata.rd
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 allNA
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 ofTriangle
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.
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