Type-2 Gumbel distribution
Probability distribution
Parameters | (real) shape (real) | ||
---|---|---|---|
CDF | |||
Mean | |||
Variance |
In probability theory, the Type-2 Gumbel probability density function is
for
- .
For the mean is infinite. For the variance is infinite.
The cumulative distribution function is
The moments exist for
The distribution is named after Emil Julius Gumbel (1891 – 1966).
Generating random variates
Given a random variate U drawn from the uniform distribution in the interval (0, 1), then the variate
has a Type-2 Gumbel distribution with parameter and . This is obtained by applying the inverse transform sampling-method.
Related distributions
- The special case b = 1 yields the Fréchet distribution.
- Substituting and yields the Weibull distribution. Note, however, that a positive k (as in the Weibull distribution) would yield a negative a and hence a negative probability density, which is not allowed.
Based on The GNU Scientific Library, used under GFDL.
See also
- Extreme value theory
- Gumbel distribution
- v
- t
- e
Probability distributions (list)
univariate
with finite support | |
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with infinite support |
univariate
univariate
continuous- discrete |
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(joint)
- Discrete:
- Ewens
- multinomial
- Continuous:
- Dirichlet
- multivariate Laplace
- multivariate normal
- multivariate stable
- multivariate t
- normal-gamma
- Matrix-valued:
- LKJ
- matrix normal
- matrix t
- matrix gamma
- Wishart
- Univariate (circular) directional
- Circular uniform
- univariate von Mises
- wrapped normal
- wrapped Cauchy
- wrapped exponential
- wrapped asymmetric Laplace
- wrapped Lévy
- Bivariate (spherical)
- Kent
- Bivariate (toroidal)
- bivariate von Mises
- Multivariate
- von Mises–Fisher
- Bingham
and singular
- Degenerate
- Dirac delta function
- Singular
- Cantor
- Category
- Commons