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

 pPiecewisePareto R Documentation

## Distribution Function of the Piecewise Pareto Distribution

### Description

Calculates the cumulative distribution function of a Piecewise Pareto Distribution

### Usage

``````pPiecewisePareto(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

``````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 April 18, 2023, 9:10 a.m.