Distance correlation coefficients for Lancaster distributions

Johannes Dueck, Dominic Edelmann and Donald Richards

Journal of Multivariate Analysis, 2017, vol. 154, issue C, 19-39

Abstract: 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.

Keywords: 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 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.jmva.2016.10.012

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