hurdlr (version 0.1)

GenPareto: The Generalized Pareto Distribution

Description

Density, distribution function, quantile function and random generation for the Generalized Pareto distribution with parameters mu, sigma, and xi.

Usage

dgpd(x, mu = 0, sigma = 1, xi = 1, log = F)
mgpd(x, mu = 0, sigma = 1, xi = 1, log = F)
pgpd(q, mu = 0, sigma = 1, xi = 1, lower.tail = T)
qgpd(p, mu = 0, sigma = 1, xi = 1, lower.tail = T)
rgpd(n, mu = 0, sigma = 1, xi = 1)

Arguments

x, q

vector of quantiles.

mu

location parameter.

sigma

(non-negative) scale parameter.

xi

shape parameter.

log

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

lower.tail

logical; if TRUE, probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).

p

numeric predictor matrix.

n

number of random values to return.

Value

dgpd gives the continuous density, pgpd gives the distribution function, qgpd gives the quantile function, and rgpd generates random deviates.

mgpd gives a probability mass function for a discretized version of GPD.

Details

The generalized pareto distribution has density $$f(x) = \frac{\sigma^{\frac{1}{\xi}}}{(\sigma + \xi(x-\mu))^{\frac{1}{\xi}+1}}$$

Examples

dexp(1,rate=.5) #Exp(rate) equivalent to gpd with mu=0 AND xi=0, and sigma=1/rate.
dgpd(1,mu=0,sigma=2,xi=0) #cannot take xi=0.
dgpd(1,mu=0,sigma=2,xi=0.0000001) #but can get close.

##"mass" function of GPD
mgpd(8) == pgpd(8.5) - pgpd(7.5)