Frechet: Create a Frechet distribution

View source: R/Frechet.R

FrechetR Documentation

Create a Frechet distribution


The Frechet distribution is a special case of the \link{GEV} distribution, obtained when the GEV shape parameter ξ is positive. It may be referred to as a type II extreme value distribution.


Frechet(location = 0, scale = 1, shape = 1)



The location (minimum) parameter m. location can be any real number. Defaults to 0.


The scale parameter s. scale can be any positive number. Defaults to 1.


The shape parameter α. shape can be any positive number. Defaults to 1.


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In the following, let X be a Frechet random variable with location parameter location = m, scale parameter scale = s, and shape parameter shape = α. A Frechet(m, s, α) distribution is equivalent to a \link{GEV}(m + s, s / α, 1 / α) distribution.

Support: (m, ∞).

Mean: m + sΓ(1 - 1/α), for α > 1; undefined otherwise.

Median: m + s(\ln 2)^(-1/α).

Variance: s^2 [Γ(1 - 2 / α) - Γ(1 - 1 / α)^2] for α > 2; undefined otherwise.

Probability density function (p.d.f):

f(x) = (α / s) [(x - m) / s] ^ [-(1 + α)] exp{-[(x - m) / s] ^ (-α)}

for x > m. The p.d.f. is 0 for x <= m.

Cumulative distribution function (c.d.f):

F(x) = exp{-[(x - m) / s] ^ (-α)}

for x > m. The c.d.f. is 0 for x <= m.


A Frechet object.

See Also

Other continuous distributions: Beta(), Cauchy(), ChiSquare(), Erlang(), Exponential(), FisherF(), GEV(), GP(), Gamma(), Gumbel(), LogNormal(), Logistic(), Normal(), RevWeibull(), StudentsT(), Tukey(), Uniform(), Weibull()



X <- Frechet(0, 2)

random(X, 10)

pdf(X, 0.7)
log_pdf(X, 0.7)

cdf(X, 0.7)
quantile(X, 0.7)

cdf(X, quantile(X, 0.7))
quantile(X, cdf(X, 0.7))

distributions3 documentation built on Sept. 7, 2022, 5:07 p.m.