Frechet {distributions3} | R Documentation |
Create a Frechet distribution
Description
The Frechet distribution is a special case of the \link{GEV}
distribution,
obtained when the GEV shape parameter is positive.
It may be referred to as a type II extreme value distribution.
Usage
Frechet(location = 0, scale = 1, shape = 1)
Arguments
location |
The location (minimum) parameter |
scale |
The scale parameter |
shape |
The shape parameter |
Details
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 be a Frechet random variable with location
parameter
location
= , scale parameter
scale
=
, and shape parameter
shape
= .
A Frechet(
) distribution is equivalent to a
\link{GEV}
() distribution.
Support: .
Mean: , for
; undefined
otherwise.
Median: .
Variance:
for
; undefined otherwise.
Probability density function (p.d.f):
for . The p.d.f. is 0 for
.
Cumulative distribution function (c.d.f):
for . The c.d.f. is 0 for
.
Value
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()
Examples
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))