# PiecewisePareto_CDF: Distribution Function of the Piecewise Pareto Distribution In Pareto: The Pareto, Piecewise Pareto and Generalized Pareto Distribution

## Description

Calculates the cumulative distribution function of a Piecewise Pareto Distribution. This function is deprecated. Use `pPiecewisePareto` instead.

## Usage

 `1` ```PiecewisePareto_CDF(x, t, alpha, truncation = NULL, truncation_type = "lp") ```

## Arguments

 `x` Numeric. The function evaluates the CDF at `x`. `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 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

Distribution function of the piecewise Pareto distribution with parameter vectors `t` and `alpha` evaluated at `x`

## 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) x <- 0:10 * 1000 pPiecewisePareto(x, t, alpha) pPiecewisePareto(x, t, alpha, truncation = 5000, truncation_type = "lp") pPiecewisePareto(x, t, alpha, truncation = 5000, truncation_type = "wd") ```

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