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

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Description

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

Usage

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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)
rgpd(n, sigma, xi, u = 0)

Arguments

x, q, p

Value, quantile or probability respectively.

n

Number of random numbers to simulate.

sigma

Scale parameter.

xi

Shape parameter.

u

Threshold

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.

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

Author(s)

Janet E Heffernan, Harry Southworth

Examples

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  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))

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