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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 Dagum distribution ： ウィキペディア英語版 Dagum distribution )^a + 1 \right)^} \right) | cdf =$\backslash right)\}^\; \backslash right)\}^$| mean =$\backslash begin$ -\frac\frac\right)\Gamma\left(\tfrac+p\right)} & \text\ a>1 \\ \text & \text\ \end | median =$b\}\backslash right)\}^\}$ | mode =$b\; \backslash right)\}^\}$| variance =$\backslash begin$ -\frac \left(2 a \frac\right) \, \Gamma\left(\tfrac + p\right)} + \left( \frac\right) \Gamma\left(\tfrac + p\right)} \right)^2\right) & \text\ a>2 \\ \text & \text\ \end | skewness =| kurtosis =| entropy =| mgf =| char =| }} The Dagum distribution is a continuous probability distribution defined over positive real numbers. It is named after Camilo Dagum, who proposed it in a series of papers in the 1970s.〔Dagum, Camilo (1975); A model of income distribution and the conditions of existence of moments of finite order; ''Bulletin of the International Statistical Institute'', 46 (Proceeding of the 40th Session of the ISI, Contributed Paper), 199-205.〕〔Dagum, Camilo (1977); A new model of personal income distribution: Specification and estimation; ''Economie Appliquée'', 30, 413-437.〕 The Dagum distribution arose from several variants of a new model on the size distribution of personal income and is mostly associated with the study of income distribution. There is both a three-parameter specification (Type I) and a four-parameter specification (Type II) of the Dagum distribution; a summary of the genesis of this distribution can be found in "A Guide to the Dagum Distributions".〔Kleiber, Christian (2008) "A Guide to the Dagum Distributions" in Chotikapanich, Duangkamon (ed.) ''Modeling Income Distributions and Lorenz Curves (Economic Studies in Inequality, Social Exclusion and Well-Being)'', Chapter 6, Springer〕 A general source on statistical size distributions often cited in work using the Dagum distribution is ''Statistical Size Distributions in Economics and Actuarial Sciences''.〔Kleiber, Christian and Samuel Kotz (2003) ''Statistical Size Distributions in Economics and Actuarial Sciences'', Wiley〕 ==Definition== The cumulative distribution function of the Dagum distribution (Type I) is given by :$F(x;a,b,p)=\; \backslash right)\}^\; \backslash right)\}^$ for $x\; >\; 0$ and where $a,\; b,\; p\; >\; 0\; .$ The corresponding probability density function is given by :$f(x;a,b,p)=\; \backslash frac\; \backslash left(\; \backslash frac)^\})^a\; +\; 1\; \backslash right)^\}\; \backslash right)\; .$ The Dagum distribution can be derived as a special case of the Generalized Beta II (GB2) distribution (a generalization of the Beta prime distribution). There is also an intimate relationship between the Dagum and Singh-Maddala distribution. :$X\; \backslash sim\; D(a,b,p)\; \backslash iff\; \backslash frac\; \backslash sim\; SM(a,\backslash tfrac,p)$ The cumulative distribution function of the Dagum (Type II) distribution adds a point mass at the origin and then follows a Dagum (Type I) distribution over the rest of the support (i.e. over the positive halfline) :$F(x;a,b,p,\backslash delta)=\; \backslash delta\; +\; (1-\backslash delta)\; \backslash right)\}^\; \backslash right)\}^\; .$ 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「Dagum 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.