triangle {apc} R Documentation

## Triangular matrices used in reserving

### Description

Triangular matrices are used for reserving in general insurance. A matrix is triangular if it is square and it has NAs in lower triangle where row+col>dim. The `apc` package uses incremental triangles.

The function `is.triangle` tests if an object is a triangular matrix.

The function `triangle.cumulative` forms the cumulative version of an incremental matrix by taking partial sums in each row.

The function `triangle.incremental` forms the incremental version of an cumulative matrix by taking differences in each row.

The function `vector.2.triangle` turns a k*(k+1)/2 vector into a triangular matrix of dimension k.

### Usage

```is.triangle(m)
triangle.cumulative(m)
triangle.incremental(m)
vector.2.triangle(v,k)```

### Arguments

 `v` vector. Length k*(k+1)/2 `k` integer. Dimension `m` matrix. Square matrix

### Author(s)

Bent Nielsen <bent.nielsen@nuffield.ox.ac.uk> 21 Nov 2019 (7 Feb 2015)

### Examples

```#########################

m <- vector.2.triangle(1:10,4)
m
is.triangle(m)
triangle.cumulative(m)
triangle.incremental(m)
```

[Package apc version 2.0.0 Index]