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 {bold x}, {bold q}, and {bold p},
respectively. rgpd
generates n random numbers, returned as an ordered vector.
Kaspar Rufibach, kaspar.rufibach@gmail.com
Samuel Mueller, mueller@maths.uwa.edu.au,
http://www.maths.usyd.edu.au/ut/people?who=S_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.