翻訳と辞書 Words near each other ・ Zeta Cephei ・ Zeta Ceti ・ Zeta Chamaeleontis ・ Zeta Chi ・ Zeta Chi Phi ・ Zeta Circini ・ Zeta Coronae Australis ・ Zeta Coronae Borealis ・ Zeta Corse ・ Zeta Corvi ・ Zeta Crateris ・ Zeta Crucis ・ Zeta Cygni ・ Zeta Delphini ・ Zeta Delta Xi ・ Zeta distribution ・ Zeta Doradus ・ Zeta Draconis ・ Zeta Equulei ・ Zeta Eridani ・ Zeta function (operator) ・ Zeta function regularization ・ Zeta function universality ・ Zeta Geminorum ・ Zeta Gruis ・ Zeta Herculis ・ Zeta Herculis Moving Group ・ Zeta Horologii ・ Zeta Hydrae ・ Zeta Hydri Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Zeta distribution ： ウィキペディア英語版 Zeta distribution | mean =$\backslash frac~\backslash textrm~s>2$| median =| mode =$1\backslash ,$| variance =$\backslash frac~\backslash textrm~s>3$| skewness =| kurtosis =| entropy =$\backslash sum\_^\backslash infty\backslash frac\backslash log\; (k^s\; \backslash zeta(s)).\backslash ,\backslash !$| mgf =$\backslash frac$| char =$\backslash frac)\}$| }} In probability theory and statistics, the zeta distribution is a discrete probability distribution. If ''X'' is a zeta-distributed random variable with parameter ''s'', then the probability that ''X'' takes the integer value ''k'' is given by the probability mass function :$f\_s(k)=k^/\backslash zeta(s)\backslash ,$ where ζ(''s'') is the Riemann zeta function (which is undefined for ''s'' = 1). The multiplicities of distinct prime factors of ''X'' are independent random variables. The Riemann zeta function being the sum of all terms $k^$ for positive integer ''k'', it appears thus as the normalization of the Zipf distribution. Indeed the terms "Zipf distribution" and the "zeta distribution" are often used interchangeably. But note that while the Zeta distribution is a probability distribution by itself, it is not associated to the Zipf's law with same exponent. See also Yule–Simon distribution == Moments == The ''n''th raw moment is defined as the expected value of ''X''''n'': :$m\_n\; =\; E(X^n)\; =\; \backslash frac\backslash sum\_^\backslash infty\; \backslash frac$ \zeta(s-n)/\zeta(s) & \textrm~n < s-1 \\ \infty & \textrm~n \ge s-1 \end \right. Note that the ratio of the zeta functions is well defined, even for ''n'' ≥ ''s'' − 1 because the series representation of the zeta function can be analytically continued. This does not change the fact that the moments are specified by the series itself, and are therefore undefined for large ''n''. 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「Zeta 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.