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, [email protected],
http://www.kasparrufibach.ch
Samuel Mueller, [email protected]
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.