ggpd {extrememix}R Documentation

The GGPD distribution

Description

Density, distribution function, quantile function and random generation for the GGPD distribution.

Usage

dggpd(x, xi, sigma, u, mu, eta, log = FALSE)

pggpd(q, xi, sigma, u, mu, eta, lower.tail = TRUE)

qggpd(p, xi, sigma, u, mu, eta, lower.tail = TRUE)

rggpd(N, xi, sigma, u, mu, eta)

Arguments

x, q

vector of quantiles.

xi

shape parameter of the tail GPD (scalar).

sigma

scale parameter of the tail GPD (scalar).

u

threshold parameter of the tail GPD (scalar).

mu

mean of the gamma bulk (scalar).

eta

shape of the gamma bulk (scalar).

log

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are P(X\leq x) otherwise P(X>x).

p

vector of probabilities.

N

number of observations.

Value

The GGPD distribution is an extreme value mixture model with density

f_{GGPD}(x|\xi,\sigma,u,\mu,\eta,w)=\left\{\begin{array}{ll} f_{GA}(x|\mu,\eta), & x\leq u \\ (1-F_{GA}(u|\mu,\eta))f_{GPD}(x|\xi,\sigma,u), &\mbox{otherwise}, \end{array}\right.

where f_{GA} is the density of the Gamma parametrized by mean \mu and shape \eta, F_{GA} is the distribution function of the Gamma and f_{GPD} is the density of the Generalized Pareto Distribution, i.e.

f_{GPD}(x|\xi,\sigma,u)=\left\{\begin{array}{ll} 1- (1+\frac{\xi}{\sigma}(x-u))^{-1/\xi}, & \mbox{if } \xi\neq 0,\\ 1- \exp\left(-\frac{x-u}{\sigma}\right), & \mbox{if } \xi = 0, \end{array}\right.

where \xi is a shape parameter, \sigma > 0 is a scale parameter and u>0 is a threshold.

dggpd gives the density, pggpd gives the distribution function, qggpd gives the quantile function, and rggpd generates random deviates. The length of the result is determined by N for rggpd and by the length of x, q or p otherwise.

References

Behrens, Cibele N., Hedibert F. Lopes, and Dani Gamerman. "Bayesian analysis of extreme events with threshold estimation." Statistical Modelling 4.3 (2004): 227-244.

Examples

dggpd(3, xi = 0.5, sigma = 2, u = 5, mu = 3, eta = 3)



[Package extrememix version 0.0.1 Index]