R: The Generalized Pareto Distribution

gpd {smoothtail}

R Documentation

The Generalized Pareto Distribution

Description

Density function, distribution function, quantile function and random generation for the generalized Pareto distribution (GPD) with shape parameter \gamma and scale parameter \sigma.

Usage

dgpd(x, gam, sigma = 1) 
pgpd(q, gam, sigma = 1) 
qgpd(p, gam, sigma = 1)
rgpd(n, gam, sigma = 1)

Arguments

`x`, `q`	Vector of quantiles.
`p`	Vector of probabilities.
`n`	Number of observations.
`gam`	Shape parameter, real number.
`sigma`	Scale parameter, positive real number.

Details

The generalized Pareto distribution function (Pickands, 1975) with shape parameter \gamma and scale parameter \sigma is

W_{\gamma,\sigma}(x) = 1 - {(1+\gamma x / \sigma)}_+^{-1/\gamma}.

If \gamma = 0, the distribution function is defined by continuity. The density is denoted by w_{\gamma, \sigma}.

Value

dgpd gives the values of the density function, pgpd those of the distribution function, and qgpd those of the quantile function of the GPD at {\bold x}, {\bold q}, and {\bold p}, respectively. rgpd generates n random numbers, returned as an ordered vector.

Author(s)

Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch

Samuel Mueller, samuel.mueller@sydney.edu.au,
www.maths.usyd.edu.au/ut/people?who=S_Mueller

References

Pickands, J. (1975). Statistical inference using extreme order statistics. Annals of Statistics, 3, 119-131.