# PiecewisePareto_Layer_Mean: Layer Mean of the Piecewise Pareto Distribution In Pareto: The Pareto, Piecewise Pareto and Generalized Pareto Distribution

## Description

Calculates the expected loss of a piecewise Pareto distribution in a reinsurance layer

## Usage

 ```1 2 3 4 5 6 7 8``` ```PiecewisePareto_Layer_Mean( Cover, AttachmentPoint, t, alpha, truncation = NULL, truncation_type = "lp" ) ```

## Arguments

 `Cover` Numeric. Cover of the reinsurance layer. `AttachmentPoint` Numeric. Attachment point of the reinsurance layer. `t` Numeric vector. Thresholds of the piecewise Pareto distribution. `alpha` Numeric vector. `alpha[i]` is the Pareto alpha in excess of `t[i]`. `truncation` Numeric. If `truncation` is not `NULL` and `truncation > t`, then the Pareto distribution is truncated at `truncation`. `truncation_type` Character. If `truncation_type = "wd"` then the whole distribution is truncated. If `truncation_type = "lp"` then a truncated Pareto is used for the last piece.

## Value

The expected loss of the (truncated) piecewise Pareto distribution with parameter vectors `t` and `alpha` in the layer `Cover` xs `AttachmentPoint`

## References

Riegel, U. (2018) Matching tower information with piecewise Pareto. European Actuarial Journal 8(2): 437–460

## Examples

 ```1 2 3 4 5 6``` ```t <- c(1000, 2000, 3000) alpha <- c(1, 1.5, 2) PiecewisePareto_Layer_Mean(4000, 1000, t, alpha) PiecewisePareto_Layer_Mean(4000, 1000, t, alpha, truncation = 5000) PiecewisePareto_Layer_Mean(4000, 1000, t, alpha, truncation = 5000, truncation_type = "lp") PiecewisePareto_Layer_Mean(4000, 1000, t, alpha, truncation = 5000, truncation_type = "wd") ```

Pareto documentation built on March 3, 2021, 5:07 p.m.