dist_gumbel
The Gumbel distribution
Description
![[Stable]](../help/figures/lifecycle-stable.svg)
Usage
dist_gumbel(alpha, scale)
Arguments
alpha |
location parameter. |
scale |
parameter. Must be strictly positive. |
Details
The Gumbel distribution is a special case of the Generalized Extreme Value distribution, obtained when the GEV shape parameter ξ is equal to 0. It may be referred to as a type I extreme value distribution.
We recommend reading this documentation on https://pkg.mitchelloharawild.com/distributional/, where the math will render nicely.
In the following, let X be a Gumbel random variable with location
parameter mu = μ, scale parameter sigma = σ.
Support: R, the set of all real numbers.
Mean: μ + σγ, where γ is Euler's constant, approximately equal to 0.57722.
Median: μ - σ ln(ln 2).
Variance: σ^2 π^2 / 6.
Probability density function (p.d.f):
f(x) = (1 / σ) exp[-(x - μ) / σ] exp{-exp[-(x - μ) / σ]}
for x in R, the set of all real numbers.
Cumulative distribution function (c.d.f):
In the ξ = 0 (Gumbel) special case
F(x) = exp{ - exp[-(x - μ) / σ]}
for x in R, 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) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7)