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

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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.

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.

n

Number of random numbers to simulate.

Details

Random number generation is done by transformation of a standard exponential.

Author(s)

Janet E Heffernan, Paul Metcalfe, 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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