texmex (version 1.1)

dgpd: Density, cumulative density, quantiles and random number generation for the generalized Pareto distribution

Description

Density, cumulative density, quantiles and random number generation for the generalized Pareto distribution

Usage

dgpd(x, sigma, xi, u = 0, log.d = FALSE)
pgpd(q, sigma, xi, u = 0, lower.tail = TRUE, log.p = FALSE)
qgpd(p, sigma, xi, u = 0, lower.tail = TRUE, log.p = FALSE)
qgpd2(p, sigma, xi, u = 0, la = 1)
rgpd(n, sigma, xi, u = 0)

Arguments

x, q, p

Value or quantile.

n

Number of random numbers to simulate.

sigma

Scale parameter.

xi

Shape parameter.

u

Threshold

la

Rate at which threshold is exceeded.

log.d, log.p

Whether or not to work on the log scale.

lower.tail

Whether to return the lower tail.

Details

The functions were originally based on code due to Stuart Coles and which appears in the ismev package. The functions have been vectorized and tested.

qgpd2 is used internally by rl.plot and is unlikely to be needed for any other reason.

Random number generation is done by inversion of the distribution function. Code written by Harry Southworth.

Examples

x <- rgpd(1000, sigma=1, xi=.5)
  hist(x)
  x <- rgpd(1000, sigma=exp(rnorm(1000, 1, .25)), xi=rnorm(1000, .5, .2))
  hist(x)
  plot(pgpd(x, sigma=1, xi=.5))