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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 Extended negative binomial distribution ： ウィキペディア英語版 Extended negative binomial distribution In probability and statistics the extended negative binomial distribution is a discrete probability distribution extending the negative binomial distribution. It is a truncated version of the negative binomial distribution〔Jonhnson, N.L.; Kotz, S.; Kemp, A.W. (1993) ''Univariate Discrete Distributions'', 2nd edition, Wiley ISBN 0-471-54897-9 (page 227)〕 for which estimation methods have been studied.〔Shah S.M. (1971) "The displaced negative binomial distribution", ''Bulletin of the Calcutta Statistical Association'', 20, 143–152〕 In the context of actuarial science, the distribution appeared in its general form in a paper by K. Hess, A. Liewald and K.D. Schmidt when they characterized all distributions for which the extended Panjer recursion works. For the case , the distribution was already discussed by Willmot and put into a parametrized family with the logarithmic distribution and the negative binomial distribution by H.U. Gerber. ==Probability mass function== For a natural number and real parameters , with and , the probability mass function of the ExtNegBin(, , ) distribution is given by :$f(k;m,r,p)=0\backslash qquad\; \backslash textk\backslash in\backslash$ and :$f(k;m,r,p)\; =\; \backslash frac\; p^k\}^\; p^j\}\backslash quad\backslash textk\backslash in\backslash textk\backslash ge\; m,$ where :$=\; \backslash frac\; =\; (-1)^k\backslash ,\backslash qquad\backslash qquad(1)$ is the (generalized) binomial coefficient and } denotes the gamma function. 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「Extended negative binomial 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.