gevdist: Generalized extreme value distribution

In mev: Modelling of Extreme Values

Generalized extreme value distribution

Description

Density function, distribution function, quantile function and random number generation for the generalized extreme value distribution.

Usage

qgev(p, loc = 0, scale = 1, shape = 0, lower.tail = TRUE, log.p = FALSE)

rgev(n, loc = 0, scale = 1, shape = 0)

dgev(x, loc = 0, scale = 1, shape = 0, log = FALSE)

pgev(q, loc = 0, scale = 1, shape = 0, lower.tail = TRUE, log.p = FALSE)

Arguments

p	vector of probabilities
loc	scalar or vector of location parameters whose length matches that of the input
scale	scalar or vector of positive scale parameters whose length matches that of the input
shape	scalar shape parameter
lower.tail	logical; if TRUE (default), returns the distribution function, otherwise the survival function
n	scalar number of observations
x, q	vector of quantiles
log, log.p	logical; if TRUE, probabilities p are given as \log(p).

Details

The distribution function of a GEV distribution with parameters loc = \mu, scale = \sigma and shape = \xi is

F(x) = \exp\{-[1 + \xi (x - \mu) / \sigma] ^ {-1/\xi} \}

for 1 + \xi (x - \mu) / \sigma > 0. If \xi = 0 the distribution function is defined as the limit as \xi tends to zero.

The quantile function, when evaluated at zero or one, returns the lower and upper endpoint, whether the latter is finite or not.

Author(s)

Leo Belzile, with code adapted from Paul Northrop

References

Jenkinson, A. F. (1955) The frequency distribution of the annual maximum (or minimum) of meteorological elements. Quart. J. R. Met. Soc., 81, 158-171. Chapter 3: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/qj.49708134804")}

Coles, S. G. (2001) An Introduction to Statistical Modeling of Extreme Values, Springer-Verlag, London. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/978-1-4471-3675-0_3")}

mev documentation built on Sept. 11, 2024, 8:14 p.m.