## Calculate Age-to-Age Factors

### Description

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(s)

Daniel Murphy

summary.ata, print.ata and chainladder

### Examples

ata(GenIns)

# Volume weighted average age-to-age factor of the "RAA" data
y <- attr(ata(RAA), "vwtd")
y
# "To ultimate" factors with a 10% tail
y <- rev(cumprod(rev(c(y, 1.1))))
names(y) <- paste(colnames(RAA), "Ult", sep="-")
y

## Label the development columns in "ratio-type" format
ata(RAA, colname.sep=":", colname.order="desc")