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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Generalized gamma distribution ： ウィキペディア英語版 Generalized gamma distribution , \mathrm\; d>1 | variance = $a^2\backslash left(\backslash frac\; -\; \backslash left(\backslash frac\backslash right)^2\backslash right)$ | skewness = | kurtosis = | entropy = $\backslash ln\; \backslash frac\; +\; \backslash frac\; +\; \backslash left(\backslash frac-\backslash frac\backslash right)\backslash psi\backslash left(\backslash frac\backslash right)$ | mgf = | cf = | pgf = | fisher = }} The generalized gamma distribution is a continuous probability distribution with three parameters. It is a generalization of the two-parameter gamma distribution. Since many distributions commonly used for parametric models in survival analysis (such as the Weibull distribution and the log-normal distribution) are special cases of the generalized gamma, it is sometimes used to determine which parametric model is appropriate for a given set of data.〔Box-Steffensmeier, Janet M.; Jones, Bradford S. (2004) ''Event History Modeling: A Guide for Social Scientists''. Cambridge University Press. ISBN 0-521-54673-7 (pp. 41-43)〕 ==Characteristics== The generalized gamma has three parameters: $a\; >\; 0$, $d\; >\; 0$, and $p\; >\; 0$. For non-negative ''x'', the probability density function of the generalized gamma is〔Stacy, E.W. (1962). "A Generalization of the Gamma Distribution." ''Annals of Mathematical Statistics'' 33(3): 1187-1192. 〕 :$$ f(x; a, d, p) = \frac}, where $\backslash Gamma(\backslash cdot)$ denotes the gamma function. The cumulative distribution function is :$$ F(x; a, d, p) = \frac , where $\backslash gamma(\backslash cdot)$ denotes the lower incomplete gamma function. If $d=p$ then the generalized gamma distribution becomes the Weibull distribution. Alternatively, if $p=1$ the generalised gamma becomes the gamma distribution. Alternative parameterisations of this distribution are sometimes used; for example with the substitution ''α  =   d/p''.〔Johnson, N.L.; Kotz, S; Balakrishnan, N. (1994) ''Continuous Univariate Distributions, Volume 1'', 2nd Edition. Wiley. ISBN 0-471-58495-9 (Section 17.8.7)〕 In addition, a shift parameter can be added, so the domain of ''x'' starts at some value other than zero.〔 If the restrictions on the signs of ''a'', ''d'' and ''p'' are also lifted (but α = ''d''/''p'' remains positive), this gives a distribution called the Amoroso distribution, after the Italian mathematician and economist Luigi Amoroso who described it in 1925.〔Gavin E. Crooks (2010), (The Amoroso Distribution ), Technical Note, Lawrence Berkeley National Laboratory.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Generalized gamma distribution」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.