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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 Chi-squared distribution ： ウィキペディア英語版 Chi-squared distribution \Gamma\left(\frac\right)}\; x^-1} e^}\, | cdf = $\backslash frac\backslash right)\}\backslash ;\backslash gamma\backslash left(\backslash frac,\backslash ,\backslash frac\backslash right)$ | mean = ''k'' | median = $\backslash approx\; k\backslash bigg(1-\backslash frac\backslash bigg)^3$ | mode = max | variance = 2''k'' | skewness = $\backslash scriptstyle\backslash sqrt\backslash ,$ | kurtosis = 12 / ''k'' | entropy = | mgf =   for  t  < ½ | char =       〔(【引用サイトリンク】 title=Characteristic function of the central chi-squared distribution )〕 }} In probability theory and statistics, the chi-squared distribution (also chi-square or ) with ''k'' degrees of freedom is the distribution of a sum of the squares of ''k'' independent standard normal random variables. It is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, e.g., in hypothesis testing or in construction of confidence intervals.〔NIST (2006). (Engineering Statistics Handbook - Chi-Squared Distribution )〕 When it is being distinguished from the more general noncentral chi-squared distribution, this distribution is sometimes called the central chi-squared distribution. The chi-squared distribution is used in the common chi-squared tests for goodness of fit of an observed distribution to a theoretical one, the independence of two criteria of classification of qualitative data, and in confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation. Many other statistical tests also use this distribution, like Friedman's analysis of variance by ranks. ==Definition== If ''Z''1, ..., ''Z''''k'' are independent, standard normal random variables, then the sum of their squares, : $$ Q\ = \sum_^k Z_i^2 , is distributed according to the chi-squared distribution with ''k'' degrees of freedom. This is usually denoted as : $$ Q\ \sim\ \chi^2(k)\ \ \text\ \ Q\ \sim\ \chi^2_k . The chi-squared distribution has one parameter: ''k'' — a positive integer that specifies the number of degrees of freedom (i.e. the number of ''Z''''i''’s) 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「Chi-squared 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.