翻訳と辞書 Words near each other ・ Gamma-Linolenic acid ・ Gamma-Melanocyte-stimulating hormone ・ Gamma-muurolene synthase ・ Gamma Control ・ Gamma Coronae Australis ・ Gamma Coronae Borealis ・ Gamma Corps ・ Gamma correction ・ Gamma Corvi ・ Gamma counter ・ Gamma Crateris ・ Gamma Crucis ・ Gamma Cygni ・ Gamma Delphini ・ Gamma delta T cell ・ Gamma distribution ・ Gamma diversity ・ Gamma Doradus ・ Gamma Doradus variable ・ Gamma Draconis ・ Gamma Epsilon Tau ・ Gamma Equulei ・ Gamma Eridani ・ Gamma Eta ・ Gamma Ethniki ・ Gamma Ethniki Cup ・ Gamma FC ・ Gamma Flight ・ Gamma function ・ Gamma Geminorum 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 Gamma distribution ： ウィキペディア英語版 Gamma distribution | cdf =$\backslash frac\; \backslash gamma\backslash left(k,\backslash ,\; \backslash frac\backslash right)$ | mean =$\backslash scriptstyle\; \backslash mathbf(X)\; =\; k\; \backslash theta$ $\backslash scriptstyle\; \backslash mathbf(X)\; =\; \backslash psi(k)\; +\backslash ln(\backslash theta)$ (see digamma function) | median =No simple closed form | mode =$\backslash scriptstyle\; (k\; \backslash ,-\backslash ,\; 1)\backslash theta\; \backslash text\; k\; \backslash ;\backslash ;\; 1$ | variance =$\backslash scriptstyle\backslash operatorname(X)\; =\; k\; \backslash theta^2$ $\backslash scriptstyle\backslash operatorname(X)\; =\; \backslash psi\_1(k)$ (see trigamma function) | skewness =$\backslash scriptstyle\; \backslash frac$ | entropy =$\backslash scriptstyle\; \backslash begin$ \scriptstyle k &\scriptstyle \,+\, \ln\theta \,+\, \ln()\\ \scriptstyle &\scriptstyle \,+\, (1 \,-\, k)\psi(k) \end | mgf = | char =$\backslash scriptstyle\; (1\; \backslash ,-\backslash ,\; \backslash theta\; i\backslash ,t)^$ | parameters2 = * α > 0 shape * β > 0 rate | support2 =$\backslash scriptstyle\; x\; \backslash ;\backslash in\backslash ;\; (0,\backslash ,\; \backslash infty)$ | pdf2 =$\backslash frac\; x^\; e^$〔http://ocw.mit.edu/courses/mathematics/18-443-statistics-for-applications-fall-2006/lecture-notes/lecture6.pdf〕 | cdf2 =$\backslash frac\; \backslash gamma(\backslash alpha,\backslash ,\; \backslash beta\; x)$ | mean2 =$\backslash scriptstyle\backslash mathbf(X)\; =\; \backslash frac$ $\backslash scriptstyle\; \backslash mathbf(X)\; =\; \backslash psi(\backslash alpha)\; -\backslash ln(\backslash beta)$ (see digamma function) | median2 =No simple closed form | mode2 =$\backslash scriptstyle\; \backslash frac\; \backslash text\; \backslash alpha\; \backslash ;\backslash ;\; 1$ | variance2 =$\backslash scriptstyle\; \backslash operatorname(X)\; =\; \backslash frac$ $\backslash scriptstyle\backslash operatorname(X)\; =\; \backslash psi\_1(\backslash alpha)$ (see trigamma function) | skewness2 =$\backslash scriptstyle\; \backslash frac$ | entropy2 =$\backslash scriptstyle\; \backslash begin$ \scriptstyle \alpha &\scriptstyle \,-\, \ln \beta \,+\, \ln()\\ \scriptstyle &\scriptstyle \,+\, (1 \,-\, \alpha)\psi(\alpha) \end | mgf2 = | char2 =$\backslash scriptstyle\; \backslash left(1\; \backslash ,-\backslash ,\; \backslash frac\backslash right)^$ }} In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The common exponential distribution and chi-squared distribution are special cases of the gamma distribution. There are three different parametrizations in common use: #With a shape parameter ''k'' and a scale parameter θ. #With a shape parameter ''α'' = ''k'' and an inverse scale parameter β = 1/θ, called a rate parameter. #With a shape parameter ''k'' and a mean parameter μ = ''k''/β. In each of these three forms, both parameters are positive real numbers. The parameterization with ''k'' and θ appears to be more common in econometrics and certain other applied fields, where e.g. the gamma distribution is frequently used to model waiting times. For instance, in life testing, the waiting time until death is a random variable that is frequently modeled with a gamma distribution.〔See Hogg and Craig (1978, Remark 3.3.1) for an explicit motivation〕 The parameterization with α and β is more common in Bayesian statistics, where the gamma distribution is used as a conjugate prior distribution for various types of inverse scale (aka rate) parameters, such as the λ of an exponential distribution or a Poisson distribution〔( ''Scalable Recommendation with Poisson Factorization'' ), Prem Gopalan, Jake M. Hofman, David Blei, arXiv.org 2014〕 – or for that matter, the β of the gamma distribution itself. (The closely related inverse gamma distribution is used as a conjugate prior for scale parameters, such as the variance of a normal distribution.) If ''k'' is an integer, then the distribution represents an Erlang distribution; i.e., the sum of ''k'' independent exponentially distributed random variables, each of which has a mean of θ (which is equivalent to a rate parameter of 1/θ). The gamma distribution is the maximum entropy probability distribution for a random variable ''X'' for which E() = ''k''θ = α/β is fixed and greater than zero, and E() = ψ(''k'') + ln(θ) = ψ(α) − ln(β) is fixed (ψ is the digamma function). ==Characterization using shape ''k'' and scale θ== A random variable ''X'' that is gamma-distributed with shape ''k'' and scale θ is denoted by :$X\; \backslash sim\; \backslash Gamma(k,\; \backslash theta)\; \backslash equiv\; \backslash textrm(k,\; \backslash theta)$ 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「Gamma 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.