Generalized Extreme Value {rmutil}

Generalized Extreme Value Distribution

Description

These functions provide information about the generalized extreme value distribution with location parameter equal to m, dispersion equal to s, and family parameter equal to f: density, cumulative distribution, quantiles, log hazard, and random generation.

The generalized extreme value distribution has density

f(y) = y^{\nu-1} \exp(y^\nu/\nu) \frac{\sigma}{\mu} \frac{\exp(y^\nu/\nu)}{\mu^{\sigma-1}/(1-I(\nu>0)+sign(\nu) exp(-\mu^-\sigma))}\exp(-(\exp(y^\nu\nu)/\mu)^\sigma)

where \mu is the location parameter of the distribution, \sigma is the dispersion, \nu is the family parameter, I() is the indicator function, and y>0.

\nu=1 a truncated extreme value distribution.

Usage

dgextval(y, s, m, f, log=FALSE)
pgextval(q, s, m, f)
qgextval(p, s, m, f)
rgextval(n, s, m, f)

Arguments

y

vector of responses.

q

vector of quantiles.

p

vector of probabilities

n

number of values to generate

m

vector of location parameters.

s

vector of dispersion parameters.

f

vector of family parameters.

log

if TRUE, log probabilities are supplied.

Author(s)

J.K. Lindsey

See Also

dweibull for the Weibull distribution.

Examples

dgextval(1, 2, 1, 2)
pgextval(1, 2, 1, 2)
qgextval(0.82, 2, 1, 2)
rgextval(10, 2, 1, 2)