Frechet: The Frechet Distribution

Description

Density, distribution function, quantile function and random generation for the Frechet distribution with location, scale and shape parameters.

Usage

dfrechet(x, loc = 0, scale = 1, shape = 1, log = FALSE)
pfrechet(q, loc = 0, scale = 1, shape = 1, lower.tail = TRUE, log.p = FALSE)
qfrechet(p, loc = 0, scale = 1, shape = 1, lower.tail = TRUE, log.p = FALSE)
rfrechet(n, loc = 0, scale = 1, shape = 1)

Value

dfrechet gives the density, pfrechet gives the distribution function, qfrechet gives the quantile function, and

rfrechet generates random deviates.

Invalid arguments will result in return value NaN, with a warning.

Arguments

x, q: vector of quantiles.
loc: location parameter.
scale: scale parameter.
shape: shape parameter.
log, log.p: logical; if TRUE, probabilities $p$ are given as $log(p)$, default: FALSE.
lower.tail: logical; if TRUE, probabilities are $P[X \le x]$ otherwise, $P[X > x]$, default: TRUE.
p: vector of probabilities.
n: number of observations.

Details

The Frechet distribution function with location parameter $m$, scale parameter $s$ and shape parameter $\alpha$ has density given by $$f(x)=\alpha/s z^(-\alpha-1) e^-z^-\alpha$$ for $x>m$, where $z=(x-m)/s$. The cumulative distribution function is $$F(x)=e^-z^-\alpha$$ for $x>m$, with $z$ as stated above.

See https://en.wikipedia.org/wiki/Frechet_distribution for more details.

Examples

Run this code

dfrechet(seq(1, 5), 0, 1, 1)
qfrechet(pfrechet(seq(1, 5), 0, 1, 1), 0, 1, 1)
rfrechet(5, 0, 1, 1)