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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 Cornish–Fisher expansion ： ウィキペディア英語版 Cornish–Fisher expansion The Cornish–Fisher expansion is an asymptotic expansion used to approximate the quantiles of a probability distribution based on its cumulants.〔 〕〔 〕〔 〕 ==Definition== For a random variable ''X'' with mean μ, variance σ², and cumulants κ''n'', its value ''yp'' at quantile ''p'' can be estimated as $y\_p\; \backslash approx\; \backslash mu\; +\; \backslash sigma\; w$ where:〔 :$$ \begin w &=& x &+ \left(h_1(x)\right )\\ &&&+ \left(h_2(x) + \gamma_1^2 h_(x)\right )\\ &&&+ \left(h_3(x) + \gamma_1\gamma_2 h_(x) + \gamma_1^3 h_(x)\right )\\ &&&+ \cdots\\ \end :$$ \begin x &= \Phi^(p)\\ \gamma_ &= \frac\\ h_1(x) &= \frac\\ h_2(x) &= \frac\\ h_(x) &= -\frac_3(x)">+ \mathrm_1(x)\right )}\\ h_3(x) &= \frac\\ h_(x) &= -\frac_4(x)">+ \mathrm_2(x)\right )}\\ h_(x) &= \frac_4(x)">+ 19\mathrm_2(x)\right )} \end where He''n'' is the ''n''th probabilists' Hermite polynomial. The values ''γ''1 and ''γ''2 are the random variable's skewness and (excess) kurtosis respectively. The value(s) in each set of brackets are the terms for that level of polynomial estimation, and all must be calculated and combined for the Cornish–Fisher expansion at that level to be valid. 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「Cornish–Fisher expansion」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.