GenPareto: The Generalized Pareto Distribution

In DescTools: Tools for Descriptive Statistics

The Generalized Pareto Distribution

Description

Density function, distribution function, quantile function and random generation for the generalized Pareto distribution (GenPareto) with location, scale and shape parameters.

Usage

dGenPareto(x, loc=0, scale=1, shape=0, log = FALSE)
pGenPareto(q, loc=0, scale=1, shape=0, lower.tail = TRUE)
qGenPareto(p, loc=0, scale=1, shape=0, lower.tail = TRUE)
rGenPareto(n, loc=0, scale=1, shape=0)

Arguments

x, q	Vector of quantiles.
p	Vector of probabilities.
n	Number of observations.
loc, scale, shape	Location, scale and shape parameters; the shape argument cannot be a vector (must have length one).
log	Logical; if TRUE, the log density is returned.
lower.tail	Logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]

Details

The generalized Pareto distribution function (Pickands, 1975) with parameters loc = a, scale = b and shape = s is

G(z) = 1 - \{1+s(z-a)/b\}^{-1/s}

for 1+s(z-a)/b > 0 and z > a, where b > 0. If s = 0 the distribution is defined by continuity.

Value

dGenPareto gives the density function, pGenPareto gives the distribution function, qGenPareto gives the quantile function, and rGenPareto generates random deviates.

Author(s)

Alec Stephenson <[e-mail]>

References

Pickands, J. (1975) Statistical inference using Extreme Order statistics. Annals of Statistics, 3, 119–131.

See Also

rGenExtrVal

Examples

dGenPareto(2:4, 1, 0.5, 0.8)
pGenPareto(2:4, 1, 0.5, 0.8)
qGenPareto(seq(0.9, 0.6, -0.1), 2, 0.5, 0.8)
rGenPareto(6, 1, 0.5, 0.8)
p <- (1:9)/10
pGenPareto(qGenPareto(p, 1, 2, 0.8), 1, 2, 0.8)
## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

DescTools documentation built on Sept. 26, 2024, 1:07 a.m.