Type-2 Gumbel distribution

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Type-2 Gumbel
Probability density function
Cumulative distribution function
Parameters (real)
shape (real)
Support
Probability density function (pdf)
Cumulative distribution function (cdf)
Mean
Median
Mode
Variance
Skewness
Excess kurtosis
Entropy
Moment-generating function (mgf)
Characteristic function

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

for

.

This implies that it similar to the Weibull distributions, substituting and . Note however that a positive k (as in the Weibull distribution) would yield a negative a, which is not allowed here as it would yield a negative probability density.

For the mean is infinite. For the variance is infinite.

The cumulative distribution function is

The moments exist for

The special case b = 1 yelds the Fréchet distribution


Based on gsl-ref_19.html#SEC309, used under GFDL.

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