Gumbel random variable

X is a Gumbel random variable if it has a probability density functionMathworldPlanetmath, given by


where -<x<, μ is the location parameter, σ is the scale parameter, and S(x) is the survivor function, S(x)=exp[-exp(x-μσ)] .

Notation for X having a Gumbel distribution is XGum(μ,σ).

: Given a Gumbel distribution XGum(μ,σ):

  1. 1.

    E[X]=μ-γσ, where γ is the Euler’s constant

  2. 2.


Remark. Nevertheless the interval (-,) in which is defined, the Gumbel distribution is often used to model reliability or lifetime of products.

Title Gumbel random variable
Canonical name GumbelRandomVariable
Date of creation 2013-03-22 15:55:40
Last modified on 2013-03-22 15:55:40
Owner georgiosl (7242)
Last modified by georgiosl (7242)
Numerical id 4
Author georgiosl (7242)
Entry type Definition
Classification msc 60E05