翻訳と辞書 Words near each other ・ Methodist New Connexion ・ Methodist Peace Fellowship ・ Methodist Protestant Church ・ Methodist Reform Church ・ Methodist Relief & Development Fund (MRDF) ・ Methodist Rome ・ Methodist Tabernacle ・ Methodist Tabernacle (Mathews, Virginia) ・ Methodist Theological School ・ Method of matched asymptotic expansions ・ Method of mean weighted residuals ・ Method of Modern Love ・ Method of Modern Love (Saint Etienne song) ・ Method of moments ・ Method of moments (probability theory) ・ Method of moments (statistics) ・ Method of normals ・ Method of quantum characteristics ・ Method of simulated moments ・ Method of steepest descent ・ Method of successive substitution ・ Method of supplementary variables ・ Method of support ・ Method of undetermined coefficients ・ Method overriding ・ Method Products ・ Method ringing ・ Method Road Soccer Stadium ・ Method stub ・ Method Studios 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 Method of moments (statistics) ： ウィキペディア英語版 Method of moments (statistics) In statistics, the method of moments is a method of estimation of population parameters. One starts with deriving equations that relate the population moments (i.e., the expected values of powers of the random variable under consideration) to the parameters of interest. Then a sample is drawn and the population moments are estimated from the sample. The equations are then solved for the parameters of interest, using the sample moments in place of the (unknown) population moments. This results in estimates of those parameters. The method of moments was introduced by Karl Pearson in 1894. ==Method== Suppose that the problem is to estimate $k$ unknown parameters $\backslash theta\_,\; \backslash theta\_,\; \backslash dots,\; \backslash theta\_$ characterizing the distribution $f\_(w;\; \backslash theta)$ of the random variable $W$.〔K. O. Bowman and L. R. Shenton, "Estimator: Method of Moments", pp 2092-2098, ''Encyclopedia of statistical sciences'', Wiley (1998).〕 Suppose the first $k$ moments of the true distribution (the "population moments") can be expressed as functions of the $\backslash theta$s: :$\backslash mu\_\; \backslash equiv\; E()=g\_(\backslash theta\_,\; \backslash theta\_,\; \backslash dots,\; \backslash theta\_)\; ,$ :$\backslash mu\_\; \backslash equiv\; E()=g\_(\backslash theta\_,\; \backslash theta\_,\; \backslash dots,\; \backslash theta\_)\; ,$ :::$\backslash vdots$ :$\backslash mu\_\; \backslash equiv\; E()=g\_(\backslash theta\_,\; \backslash theta\_,\; \backslash dots,\; \backslash theta\_)\; .$ Suppose a sample of size $n$ is drawn, resulting in the values $w\_1,\; \backslash dots,\; w\_n$. For $j=1,\backslash dots,k$, let :$\backslash hat\_=\backslash frac\backslash sum\_^\; w\_^$ be the j-th sample moment, an estimate of $\backslash mu\_$. The method of moments estimator for $\backslash theta\_,\; \backslash theta\_,\; \backslash dots,\; \backslash theta\_$ denoted by $\backslash hat\_,\; \backslash hat\_,\; \backslash dots,\; \backslash hat\_$ is defined as the solution (if there is one) to the equations: :$\backslash hat\; \backslash mu\_\; =\; g\_(\backslash hat\_,\; \backslash hat\_,\; \backslash dots,\; \backslash hat\_)\; ,$ :$\backslash hat\; \backslash mu\_\; =\; g\_(\backslash hat\_,\; \backslash hat\_,\; \backslash dots,\; \backslash hat\_)\; ,$ :::$\backslash vdots$ :$\backslash hat\; \backslash mu\_\; =\; g\_(\backslash hat\_,\; \backslash hat\_,\; \backslash dots,\; \backslash hat\_)\; .$ 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「Method of moments (statistics)」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.