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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 Normal-inverse Gaussian distribution ： ウィキペディア英語版 Normal-inverse Gaussian distribution \; e^ $K\_j$ denotes a modified Bessel function of the third kind〔Ole E Barndorff-Nielsen, Thomas Mikosch and Sidney I. Resnick, Lévy Processes: Theory and Applications, Birkhäuser 2013 ''Note: in the literature this function is also referred to as Modified Bessel function of the third kind''〕| cdf =| mean =$\backslash mu\; +\; \backslash delta\; \backslash beta\; /\; \backslash gamma$| median =| mode =| variance =$\backslash delta\backslash alpha^2/\backslash gamma^3$| skewness =$3\; \backslash beta\; /(\backslash alpha\; \backslash sqrt)$| kurtosis =$3(1+4\; \backslash beta^2/\backslash alpha^2)/(\backslash delta\backslash gamma)$| entropy =| mgf =$e^$| char =$e^$| }} The normal-inverse Gaussian distribution (NIG) is continuous probability distribution that is defined as the normal variance-mean mixture where the mixing density is the inverse Gaussian distribution. The NIG distribution was noted by Blaesild in 1977 as a subclass of the generalised hyperbolic distribution discovered by Ole Barndorff-Nielsen, in the next year Barndorff-Nielsen published the NIG in another paper.〔O. Barndorff-Nielsen, Hyperbolic Distributions and Distributions on Hyperbolae, Scandinavian Journal of Statistics 1978〕 It was introduced in the mathematical finance literature in 1997.〔O. Barndorff-Nielsen, Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling, Scandinavian Journal of Statistics 1997〕 The parameters of the normal-inverse Gaussian distribution are often used to construct a heaviness and skewness plot called the NIG-triangle.〔S.T Rachev, Handbook of Heavy Tailed Distributions in Finance, Volume 1: Handbooks in Finance, Book 1, North Holland 2003〕 ==Properties== 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「Normal-inverse Gaussian 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.