Frechet: The Frechet Distribution

In DescTools: Tools for Descriptive Statistics

The Frechet Distribution

Description

Density function, 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)
qFrechet(p, loc=0, scale=1, shape=1, lower.tail = TRUE)
rFrechet(n, loc=0, scale=1, shape=1)

Arguments

x, q	Vector of quantiles.
p	Vector of probabilities.
n	Number of observations.
loc, scale, shape	Location, scale and shape parameters (can be given as vectors).
log	Logical; if TRUE, the log density is returned.
lower.tail	Logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]

Details

The Frechet distribution function with parameters loc = a, scale = b and shape = s is

G(z) = \exp\left\{-\left(\frac{z-a}{b}\right)^{-s} \right\}

for z > a and zero otherwise, where b > 0 and s > 0.

Value

dFrechet gives the density function, pFrechet gives the distribution function, qFrechet gives the quantile function, and rFrechet generates random deviates.

Author(s)

Alec Stephenson <[e-mail]>

See Also

rGenExtrVal, rGumbel, rRevWeibull

Examples

dFrechet(2:4, 1, 0.5, 0.8)
pFrechet(2:4, 1, 0.5, 0.8)
qFrechet(seq(0.9, 0.6, -0.1), 2, 0.5, 0.8)
rFrechet(6, 1, 0.5, 0.8)
p <- (1:9)/10
pFrechet(qFrechet(p, 1, 2, 0.8), 1, 2, 0.8)
## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

DescTools documentation built on Sept. 26, 2024, 1:07 a.m.