Type-2 Gumbel distribution

In probability theory, the Type-2 Gumbel probability density function is

Type-2 Gumbel
Parameters (real)
shape (real)
PDF
CDF
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 edit

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 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.

See also edit