翻訳と辞書 Words near each other ・ Conway, Massachusetts ・ Conway, Missouri ・ Conway, New Hampshire ・ Conway, North Carolina ・ Conway, North Dakota ・ Conway, Nova Scotia ・ Conway, Pennsylvania ・ Conway, South Carolina ・ Conway, Texas ・ Conway, the Kerry Dancer ・ Conway, Washington ・ Conway-class corvette ・ Conway-class post ship ・ Conway-Robinson State Forest ・ Conway–Horry County Airport ・ Conway–Maxwell–Poisson distribution ・ Conwell ・ Conwell-Egan Catholic High School ・ Conwil railway station ・ CONWIP ・ Conwoïon ・ Conwy ・ Conwy & Denbighshire NHS Trust ・ Conwy (disambiguation) ・ Conwy (National Assembly for Wales constituency) ・ Conwy (UK Parliament constituency) ・ Conwy Bay ・ Conwy Borough F.C. ・ Conwy Castle ・ Conwy Celts 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 Conway–Maxwell–Poisson distribution ： ウィキペディア英語版 Conway–Maxwell–Poisson distribution In probability theory and statistics, the Conway–Maxwell–Poisson (CMP or COM-Poisson) distribution is a discrete probability distribution named after Richard W. Conway, William L. Maxwell, and Siméon Denis Poisson that generalizes the Poisson distribution by adding a parameter to model overdispersion and underdispersion. It is a member of the exponential family, has the Poisson distribution and geometric distribution as special cases and the Bernoulli distribution as a limiting case. The COM-Poisson distribution was originally proposed by Conway and Maxwell in 1962 as a solution to handling queueing systems with state-dependent service rates. The probabilistic and statistical properties of the distribution were published by Shmueli et al. (2005).〔Shmueli G., Minka T., Kadane J.B., Borle S., and Boatwright, P.B. "A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution." Journal of the Royal Statistical Society: Series C (Applied Statistics) 54.1 (2005): 127–142.()〕 The COM-Poisson is defined to be the distribution with probability mass function :$$ \Pr(X = x) = f(x; \lambda, \nu) = \frac\frac, for ''x'' = 0,1,2,..., $\backslash lambda\; >\; 0$ and $\backslash nu$ ≥ 0, where :$$ Z(\lambda,\nu) = \sum_^\infty \frac. The function $Z(\backslash lambda,\backslash nu)$ serves as a normalization constant so the probability mass function sums to one. Note that $Z(\backslash lambda,\backslash nu)$ does not have a closed form. The additional parameter $\backslash nu$ which does not appear in the Poisson distribution allows for adjustment of the rate of decay. This rate of decay is a non-linear decrease in ratios of successive probabilities, specifically :$$ \frac = \frac. When $\backslash nu\; =\; 1$, the COM-Poisson distribution becomes the standard Poisson distribution and as $\backslash nu\; \backslash to\; \backslash infty$, the distribution approaches a Bernoulli distribution with parameter $\backslash lambda/(1+\backslash lambda)$. When $\backslash nu=0$ the CoM-Poisson distribution reduces to a geometric distribution with probability of success $1-\backslash lambda$ provided . For the COM-Poisson distribution, moments can be found through the recursive formula :$$ \operatorname() = \begin \lambda \, \operatorname()^ & \text r = 0 \\ \lambda \, \frac\operatorname() + \operatorname()\operatorname() & \text r > 0. \\ \end == Parameter estimation == There are a few methods of estimating the parameters of the CMP distribution from the data. Two methods will be discussed: weighted least squares and maximum likelihood. The weighted least squares approach is simple and efficient but lacks precision. Maximum likelihood, on the other hand, is precise, but is more complex and computationally intensive. 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「Conway–Maxwell–Poisson 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.