Distance correlation coefficients for Lancaster distributions

JOURNAL OF MULTIVARIATE ANALYSIS

卷:154

Article

Dueck, Johannes¹  Edelmann, Dominic²  Richards, Donald³ 

[1] Heidelberg Univ, Inst Appl Math, Neuenheimer Feld 294, D-69120 Heidelberg, Germany

[2] German Canc Res Ctr, Div Biostat, Neuenheimer Feld 280, D-69120 Heidelberg, Germany

[3] Penn State Univ, Dept Stat, University Pk, PA 16802 USA

关键词: Affine invariance;    Bivariate gamma distribution;    Bivariate normal distribution;    Bivariate negative binomial distribution;    Bivariate Poisson distribution;    Characteristic function;    Distance correlation coefficient;    Lancaster distributions;    Multivariate normal distribution;   

DOI  :  10.1016/j.jmva.2016.10.012

来源: Elsevier

【 摘 要 】

We consider the problem of calculating distance correlation coefficients between random vectors whose joint distributions belong to the class of Lancaster distributions. We derive under mild convergence conditions a general series representation for the distance covariance for these distributions. To illustrate the general theory, we apply the series representation to derive explicit expressions for the distance covariance and distance correlation coefficients for the bivariate normal distribution and its generalizations of Lancaster type, the multivariate normal distributions, and the bivariate gamma, Poisson, and negative binomial distributions which are of Lancaster type. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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