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Milds # Type-2 Gumbel distribution

Parameters $a\!$ (real)$b\!$ shape (real) $abx^{-a-1}e^{-bx^{-a}}\!$ $e^{-bx^{-a}}\!$ $b^{1/a}\Gamma (1-1/a)\!$ $b^{2/a}(\Gamma (1-1/a)-{\Gamma (1-1/a)}^{2})\!$ In probability theory, the Type-2 Gumbel probability density function is

$f(x|a,b)=abx^{-a-1}e^{-bx^{-a}}\,$ for

$0 .

This implies that it is similar to the Weibull distributions, substituting $b=\lambda ^{-k}$ and $a=-k$ . 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 $0 the mean is infinite. For $0 the variance is infinite.

$F(x|a,b)=e^{-bx^{-a}}\,$ The moments $E[X^{k}]\,$ exist for $k The special case b = 1 yields the Fréchet distribution.

Based on The GNU Scientific Library, used under GFDL.

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#### Transcription This page was last edited on 13 April 2018, at 01:16