dist_gumbel {distributional} | R Documentation |
The Gumbel distribution
Description
The Gumbel distribution is a special case of the Generalized Extreme Value
distribution, obtained when the GEV shape parameter is equal to 0.
It may be referred to as a type I extreme value distribution.
Usage
dist_gumbel(alpha, scale)
Arguments
alpha |
location parameter. |
scale |
parameter. Must be strictly positive. |
Details
We recommend reading this documentation on https://pkg.mitchelloharawild.com/distributional/, where the math will render nicely.
In the following, let be a Gumbel random variable with location
parameter
mu
= , scale parameter
sigma
= .
Support: , the set of all real numbers.
Mean: , where
is Euler's
constant, approximately equal to 0.57722.
Median: .
Variance: .
Probability density function (p.d.f):
for in
, the set of all real numbers.
Cumulative distribution function (c.d.f):
In the (Gumbel) special case
for in
, the set of all real numbers.
See Also
Examples
dist <- dist_gumbel(alpha = c(0.5, 1, 1.5, 3), scale = c(2, 2, 3, 4))
dist
mean(dist)
variance(dist)
skewness(dist)
kurtosis(dist)
support(dist)
generate(dist, 10)
density(dist, 2)
density(dist, 2, log = TRUE)
cdf(dist, 4)
quantile(dist, 0.7)