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・ Generation effect
・ Generation EFX
・ Generalized game theory
・ Generalized gamma distribution
・ Generalized Gauss–Bonnet theorem
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・ Generalized Hebbian Algorithm
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・ Generalized inverse
Generalized inverse Gaussian distribution
・ Generalized inversive congruential pseudorandom numbers
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Generalized inverse Gaussian distribution : ウィキペディア英語版
Generalized inverse Gaussian distribution
x^ e^|
cdf =|
mean =\frac(\sqrt) }(\sqrt)}|
median =|
mode =\frac|
variance =\left(\frac\right)\left()|
skewness =|
kurtosis =|
entropy =|
mgf =\left(\frac\right)^}\frac|
char =\left(\frac\right)^}\frac|
}}
In probability theory and statistics, the generalized inverse Gaussian distribution (GIG) is a three-parameter family of continuous probability distributions with probability density function
:f(x) = \frac)} x^ e^,\qquad x>0,
where ''Kp'' is a modified Bessel function of the second kind, ''a'' > 0, ''b'' > 0 and ''p'' a real parameter. It is used extensively in geostatistics, statistical linguistics, finance, etc. This distribution was first proposed by Étienne Halphen.〔
〕〔Étienne Halphen was the uncle of the mathematician Georges Henri Halphen.〕
It was rediscovered and popularised by Ole Barndorff-Nielsen, who called it the generalized inverse Gaussian distribution. It is also known as the Sichel distribution, after Herbert Sichel.〔Sichel, H.S., Statistical valuation of diamondiferous deposits, Journal of the South African Institute of Mining and Metallurgy 1973〕 Its statistical properties are discussed in Bent Jørgensen's lecture notes.〔

==Properties==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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