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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 Singh-Maddala distribution ： ウィキペディア英語版 Burr distribution | mean =$\backslash mu\_1=k\backslash operatorname(k-1/c,\backslash ,\; 1+1/c)$ where Β() is the beta function| median =$\backslash left(2^\}-1\backslash right)^\backslash frac$| mode =$\backslash left(\backslash frac\backslash right)^\backslash frac$| variance =$-\backslash mu\_1^2+\backslash mu\_2$| skewness =$2\backslash mu\_1^3-3\backslash mu\_1\backslash mu\_2+\backslash mu\_3$| kurtosis =$-3\backslash mu\_1^4+6\backslash mu\_1^2\backslash mu\_2-4\backslash mu\_1\backslash mu\_3+\backslash mu\_4$ where moments ((see )) $\backslash mu\_r\; =k\backslash operatorname\backslash left(\backslash frac,\backslash ,\; \backslash frac\backslash right)$| entropy =| mgf =| char =| }} In probability theory, statistics and econometrics, the Burr Type XII distribution or simply the Burr distribution is a continuous probability distribution for a non-negative random variable. It is also known as the Singh–Maddala distribution and is one of a number of different distributions sometimes called the "generalized log-logistic distribution". It is most commonly used to model household income (See: Household income in the U.S. and compare to magenta graph at right). The Burr (Type XII) distribution has probability density function: :$f(x;c,k)\; =\; ck\backslash frac\}\backslash !$ and cumulative distribution function: :$F(x;c,k)\; =\; 1-\backslash left(1+x^c\backslash right)^\; .$ Note when ''c''=1, the Burr distribution becomes the Pareto Type II distribution. When ''k''=1, the Burr distribution is a special case of the Champernowne distribution, often referred to as the Fisk distribution.〔 See Sections 7.3 "Champernowne Distribution" and 6.4.1 "Fisk Distribution."〕 The Burr Type XII distribution is a member of a system of continuous distributions introduced by Irving W. Burr (1942), which comprises 12 distributions.〔See Kleiber and Kotz (2003), Table 2.4, p. 51, "The Burr Distributions."〕 == See also == *Dagum distribution, also known as the inverse Burr Distribution. 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「Burr 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.