# EPdist: The Extended Pareto Distribution In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

 Extended Pareto R Documentation

## The Extended Pareto Distribution

### Description

Density, distribution function, quantile function and random generation for the Extended Pareto Distribution (EPD).

### Usage

depd(x, gamma, kappa, tau = -1, log = FALSE)
pepd(x, gamma, kappa, tau = -1, lower.tail = TRUE, log.p = FALSE)
qepd(p, gamma, kappa, tau = -1, lower.tail = TRUE, log.p = FALSE)
repd(n, gamma, kappa, tau = -1)


### Arguments

 x Vector of quantiles. p Vector of probabilities. n Number of observations. gamma The \gamma parameter of the EPD, a strictly positive number. kappa The \kappa parameter of the EPD. It should be larger than \max\{-1,1/\tau\}. tau The \tau parameter of the EPD, a strictly negative number. Default is -1. log Logical indicating if the densities are given as \log(f), default is FALSE. lower.tail Logical indicating if the probabilities are of the form P(X\le x) (TRUE) or P(X>x) (FALSE). Default is TRUE. log.p Logical indicating if the probabilities are given as \log(p), default is FALSE.

### Details

The Cumulative Distribution Function (CDF) of the EPD is equal to F(x) = 1-(x(1+\kappa-\kappa x^{\tau}))^{-1/\gamma} for all x > 1 and F(x)=0 otherwise.

Note that an EPD random variable with \tau=-1 and \kappa=\gamma/\sigma-1 is GPD distributed with \mu=1, \gamma and \sigma.

### Value

depd gives the density function evaluated in x, pepd the CDF evaluated in x and qepd the quantile function evaluated in p. The length of the result is equal to the length of x or p.

repd returns a random sample of length n.

Tom Reynkens.

### References

Beirlant, J., Joossens, E. and Segers, J. (2009). "Second-Order Refined Peaks-Over-Threshold Modelling for Heavy-Tailed Distributions." Journal of Statistical Planning and Inference, 139, 2800–2815.

Pareto, GPD, Distributions

### Examples

# Plot of the PDF
x <- seq(0, 10, 0.01)
plot(x, depd(x, gamma=1/2, kappa=1, tau=-1), xlab="x", ylab="PDF", type="l")

# Plot of the CDF
x <- seq(0, 10, 0.01)
plot(x, pepd(x, gamma=1/2, kappa=1, tau=-1), xlab="x", ylab="CDF", type="l")


ReIns documentation built on March 31, 2023, 8:09 p.m.