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Distance correlation coefficients for Lancaster distributions

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. T...

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Hauptverfasser: Dueck, Johannes (VerfasserIn) , Edelmann, Dominic (VerfasserIn) , Richards, Donald (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: February 2017
In: Journal of multivariate analysis
Year: 2016, Jahrgang: 154, Pages: 19-39
ISSN:1095-7243
DOI:10.1016/j.jmva.2016.10.012
Online-Zugang:Verlag, Volltext: http://dx.doi.org/10.1016/j.jmva.2016.10.012
Verlag, Volltext: http://www.sciencedirect.com/science/article/pii/S0047259X16301245
Volltext
Verfasserangaben:Johannes Dueck, Dominic Edelmann, and Donald Richards

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520 |a 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. 
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