Density function, distribution function, quantile function and random generation for the generalized Pareto distribution (GPD) with shape parameter \(\gamma\) and scale parameter \(\sigma\).
dgpd(x, gam, sigma = 1)
pgpd(q, gam, sigma = 1)
qgpd(p, gam, sigma = 1)
rgpd(n, gam, sigma = 1)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.
Vector of quantiles.
Vector of probabilities.
Number of observations.
Shape parameter, real number.
Scale parameter, positive real number.
Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch
Samuel Mueller, samuel.muller@mq.edu.au
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 \(w_{\gamma, \sigma}\).
Pickands, J. (1975). Statistical inference using extreme order statistics. Annals of Statistics, 3, 119-131.
Similar functions are provided in the R-packages evir and evd.