In probability theory, the Type-2 Gumbel probability density function is
Parameters |
(real) shape (real) | ||
---|---|---|---|
CDF | |||
Quantile | |||
Mean | |||
Variance |
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
editGiven 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
edit- 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.