Frechet | R Documentation |
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)
location |
The location (minimum) parameter m.
|
scale |
The scale parameter s.
|
shape |
The shape parameter α.
|
We recommend reading this documentation on https://alexpghayes.github.io/distributions3/, where the math will render with additional detail and much greater clarity.
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.
Other continuous distributions:
Beta()
,
Cauchy()
,
ChiSquare()
,
Erlang()
,
Exponential()
,
FisherF()
,
GEV()
,
GP()
,
Gamma()
,
Gumbel()
,
LogNormal()
,
Logistic()
,
Normal()
,
RevWeibull()
,
StudentsT()
,
Tukey()
,
Uniform()
,
Weibull()
set.seed(27) X <- Frechet(0, 2) X 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))
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