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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 L-kurtosis ： ウィキペディア英語版 L-moment In statistics, L-moments are a sequence of statistics used to summarize the shape of a probability distribution.〔Asquith, W.H. (2011) ''Distributional analysis with L-moment statistics using the R environment for statistical computing'', Create Space Independent Publishing Platform, (), ISBN 1-463-50841-7〕 They are linear combinations of order statistics (L-statistics) analogous to conventional moments, and can be used to calculate quantities analogous to standard deviation, skewness and kurtosis, termed the L-scale, L-skewness and L-kurtosis respectively (the L-mean is identical to the conventional mean). Standardised L-moments are called L-moment ratios and are analogous to standardized moments. Just as for conventional moments, a theoretical distribution has a set of population L-moments. Sample L-moments can be defined for a sample from the population, and can be used as estimators of the population L-moments. ==Population L-moments== For a random variable ''X'', the ''r''th population L-moment is〔 :$$ \lambda_r = r^ \sum_^ \mathrmX_}, where ''X''''k:n'' denotes the ''k''th order statistic (''k''th smallest value) in an independent sample of size ''n'' from the distribution of ''X'' and $\backslash mathrm$ denotes expected value. In particular, the first four population L-moments are :$$ \lambda_1 = \mathrmX :$$ \lambda_2 = (\mathrmX_ - \mathrmX_)/2 :$$ \lambda_3 = (\mathrmX_ - 2\mathrmX_ + \mathrmX_)/3 :$$ \lambda_4 = (\mathrmX_ - 3\mathrmX_ + 3\mathrmX_ - \mathrmX_)/4. Note that the coefficients of the ''k''-th L-moment are the same as in the ''k''-th term of the binomial transform, as used in the ''k''-order finite difference (finite analog to the derivative). The first two of these L-moments have conventional names: :$\backslash lambda\_1\; =\; \backslash text,$ :$\backslash lambda\_2\; =\; \backslash text.$ The L-scale is equal to half the mean difference.〔 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「L-moment」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.