Distance correlation coefficients for Lancaster distributions

Johannes Dueck, Dominic Edelmann, Donald Richards

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)19-39
Number of pages21
JournalJournal of Multivariate Analysis
Volume154
DOIs
StatePublished - Feb 1 2017

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Normal distribution
Correlation coefficient
Series Representation
Bivariate Normal Distribution
Negative binomial distribution
Convergence Condition
Multivariate Normal Distribution
Random Vector
Joint Distribution
Siméon Denis Poisson

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

Cite this

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Distance correlation coefficients for Lancaster distributions. / Dueck, Johannes; Edelmann, Dominic; Richards, Donald.

In: Journal of Multivariate Analysis, Vol. 154, 01.02.2017, p. 19-39.

Research output: Contribution to journalArticle

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AU - Richards, Donald

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AB - 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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