“Fisher-Tippett Distribution”的概念、定义、习题解题方法及翻译-数学辞典

单词

Fisher-Tippett Distribution

释义

Fisher-Tippett Distribution

Also called the Extreme Value Distribution and Log-Weibull Distribution. It is the limiting distributionfor 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)

where

is the Gamma Function. The special case of the Fisher-Tippett distribution with

is calledGumbel's Distribution.

See also Euler-Mascheroni Integrals, Gumbel's Distribution

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