gpd: The Generalized Pareto Distribution
In smoothtail: Smooth Estimation of GPD Shape Parameter

Description Usage Arguments Details Value Author(s) References See Also

Density function, distribution function, quantile function and random generation for the generalized Pareto distribution (GPD) with shape parameter γ 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 γ and scale parameter σ is

W_{γ,σ}(x) = 1 - {(1+γ x / σ)}_+^{-1/γ}.

If γ = 0, the distribution function is defined by continuity. The density is denoted by w_{γ, 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,
http://www.kasparrufibach.ch

Samuel Mueller, samuel.mueller@sydney.edu.au,
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.

smoothtail documentation built on May 2, 2019, 5:41 a.m.