GenPARETO {FAdist}

Generalized Pareto Distribution

Description

Density, distribution function, quantile function and random generation for the generalized Pareto distribution with shape and scale parameters equal to shape and scale, respectively.

Usage

dgp(x,shape=1,scale=1,log=FALSE)
pgp(q,shape=1,scale=1,lower.tail=TRUE,log.p=FALSE)
qgp(p,shape=1,scale=1,lower.tail=TRUE,log.p=FALSE)
rgp(n,shape=1,scale=1)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations.

shape

shape parameter.

scale

scale parameter.

log, log.p

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

lower.tail

logical; if TRUE (default), probabilities are P[X <= x],otherwise, P[X > x].

Details

If X is a random variable distributed according to a generalized Pareto distribution, it has density
f(x) = 1/scale*(1-shape*x/scale)^((1-shape)/shape)

Value

dgp gives the density, pgp gives the distribution function, qgp gives the quantile function, and rgp generates random deviates.

References

Coles, S. (2001) An introduction to statistical modeling of extreme values. Springer

Examples

x <- rgp(1000,-.2,10)
hist(x,freq=FALSE,col='gray',border='white')
curve(dgp(x,-.2,10),add=TRUE,col='red4',lwd=2)