gpd {smoothtail} | R Documentation |
Density function, distribution function, quantile function and random generation for the generalized Pareto distribution (GPD) with shape parameter gamma and scale parameter σ.
dgpd(x, gam, sigma = 1) pgpd(q, gam, sigma = 1) qgpd(p, gam, sigma = 1) rgpd(n, gam, sigma = 1)
x, q |
Vector of quantiles. |
p |
Vector of probabilities. |
n |
Number of observations. |
gam |
Shape parameter, real number. |
sigma |
Scale parameter, positive real number. |
The generalized Pareto distribution function (Pickands, 1975) with shape parameter gamma and scale parameter σ is
W_{gamma,σ}(x) = 1 - {(1+gamma x / σ)}_+^{-1/gamma}.
If gamma = 0, the distribution function is defined by continuity. The density is denoted by w_{gamma, σ}.
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 x, q, and p,
respectively. rgpd
generates n random numbers, returned as an ordered vector.
Kaspar Rufibach, kaspar.rufibach@stanford.edu,
http://www.stanford.edu/~kasparr
Samuel Mueller, mueller@maths.uwa.edu.au,
http://www.maths.uwa.edu.au/Members/mueller
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.