# Frechet: Frechet distribution In extraDistr: Additional Univariate and Multivariate Distributions

## Description

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

## Usage

 ```1 2 3 4 5 6 7``` ```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 ≤ 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) = λ/σ * ((x-μ)/σ)^(-1-λ) * exp(-((x-μ)/σ)^-λ)

Cumulative distribution function

F(x) = exp(-((x-μ)/σ)^-λ)

Quantile function

F^-1(p) = μ + σ * -log(p)^{-1/λ}

## References

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

## Examples

 ```1 2 3 4 5 6 7``` ```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) ```

extraDistr documentation built on Sept. 7, 2020, 5:09 p.m.