## 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")

```