Also called the Extreme Value Distribution and Log-Weibull Distribution. It is the limiting distribution
for the smallest or largest values in a large sample drawn from a variety of distributions.

(1) | |||

(2) |

These can be computed directly be defining

(3) | |||

(4) | |||

(5) |

Then the Moments are

(6) |

where are Euler-Mascheroni Integrals. Plugging in the Euler-Mascheroni Integrals gives

(7) | |||

(8) | |||

(9) | |||

(10) | |||

(11) |

where is the Euler-Mascheroni Constant and is Apéry's Constant. The Mean, Variance, Skewness, and Kurtosis are therefore

(12) | |||

(13) | |||

(14) | |||

(15) |

The Characteristic Function is

(16) |

© 1996-9

1999-05-26