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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 Holtsmark distribution ： ウィキペディア英語版 Holtsmark distribution The (one-dimensional) Holtsmark distribution is a continuous probability distribution. The Holtsmark distribution is a special case of a stable distribution with the index of stability or shape parameter $\backslash alpha$ equal to 3/2 and skewness parameter $\backslash beta$ of zero. Since $\backslash beta$ equals zero, the distribution is symmetric, and thus an example of a symmetric alpha-stable distribution. The Holtsmark distribution is one of the few examples of a stable distribution for which a closed form expression of the probability density function is known. However, its probability density function is not expressible in terms of elementary functions; rather, the probability density function is expressed in terms of hypergeometric functions. The Holtsmark distribution has applications in plasma physics and astrophysics.〔 In 1919, Norwegian physicist J. Holtsmark proposed the distribution as a model for the fluctuating fields in plasma due to chaotic motion of charged particles. It is also applicable to other types of Coulomb forces, in particular to modeling of gravitating bodies, and thus is important in astrophysics. ==Characteristic function== The characteristic function of a symmetric stable distribution is: : $$ \varphi(t;\mu,c) = \exp\left(t|^\alpha~\right ), where $\backslash alpha$ is the shape parameter, or index of stability, $\backslash mu$ is the location parameter, and ''c'' is the scale parameter. Since the Holtsmark distribution has $\backslash alpha=3/2,$ its characteristic function is: : $$ \varphi(t;\mu,c) = \exp\left(t|^~\right ) . Since the Holtsmark distribution is a stable distribution with , $\backslash mu$ represents the mean of the distribution. Since , $\backslash mu$ also represents the median and mode of the distribution. And since , the variance of the Holtsmark distribution is infinite.〔 All higher moments of the distribution are also infinite.〔 Like other stable distributions (other than the normal distribution), since the variance is infinite the dispersion in the distribution is reflected by the scale parameter, c. An alternate approach to describing the dispersion of the distribution is through fractional moments.〔 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「Holtsmark 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.