Frechet function

Frechet distribution

Frechet distribution

Density, distribution function, quantile function and random generation for the Frechet distribution.


dfrechet(x, lambda = 1, mu = 0, sigma = 1, log = FALSE)

pfrechet(q, lambda = 1, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)

qfrechet(p, lambda = 1, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)

rfrechet(n, lambda = 1, mu = 0, sigma = 1)

Arguments

x, q: vector of quantiles.
lambda, sigma, mu: shape, scale, and location parameters. Scale and shape must be positive.
log, log.p: logical; if TRUE, probabilities p are given as log(p).
lower.tail: logical; if TRUE (default), probabilities are $P[X \le x]$

otherwise, $P[X > x]$ .
p: vector of probabilities.
n: number of observations. If length(n) > 1, the length is taken to be the number required.

Details

Probability density function

f(x) = \frac{\lambda}{\sigma} \left(\frac{x-\mu}{\sigma}\right)^{-1-\lambda} \exp\left(-\left(\frac{x-\mu}{\sigma}\right)^{-\lambda}\right)f(x) = \lambda/\sigma * ((x-\mu)/\sigma)^(-1-\lambda) * exp(-((x-\mu)/\sigma)^-\lambda)

Cumulative distribution function

F(x) = \exp\left(-\left(\frac{x-\mu}{\sigma}\right)^{-\lambda}\right)F(x) = exp(-((x-\mu)/\sigma)^-\lambda)

Quantile function

F^{-1}(p) = \mu + \sigma -\log(p)^{-1/\lambda}F^-1(p) = \mu + \sigma * -log(p)^{-1/\lambda}

Examples


x <- rfrechet(1e5, 5, 2, 1.5)
xx <- seq(0, 1000, by = 0.1)
hist(x, 200, freq = FALSE)
lines(xx, dfrechet(xx, 5, 2, 1.5), col = "red") 
hist(pfrechet(x, 5, 2, 1.5))
plot(ecdf(x))
lines(xx, pfrechet(xx, 5, 2, 1.5), col = "red", lwd = 2)

References

Bury, K. (1999). Statistical Distributions in Engineering. Cambridge University Press.

extraDistr package Read PDF manual

Maintainer: Tymoteusz Wolodzko
License: GPL-2
Last published: 2023-11-30

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