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Two multivariate generalized beta families

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  • William M. Cockriel
  • James B. McDonald

Abstract

A multivariate generalized beta distribution is introduced that extends the univariate generalized beta distribution and includes many multivariate distributions, such as the multivariate beta of the first and second kind, the generalized gamma, and the Burr and Dirichlet distributions as special and limiting cases. These interrelationships can be illustrated using a distributional family tree. The corresponding marginal distributions are univariate generalized beta distributions and their special cases. Selected expressions for the moments are reported, and an application to the joint distribution of income and wealth is presented. A simple transformation of the multivariate generalized beta distribution leads to what will be referred to as a multivariate exponential generalized beta distribution, which includes a multivariate form of the logistics and Burr distributions as special cases.

Suggested Citation

  • William M. Cockriel & James B. McDonald, 2018. "Two multivariate generalized beta families," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(23), pages 5688-5701, December.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:23:p:5688-5701
    DOI: 10.1080/03610926.2017.1400058
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    Cited by:

    1. José María Sarabia & Vanesa Jordá & Faustino Prieto & Montserrat Guillén, 2020. "Multivariate Classes of GB2 Distributions with Applications," Mathematics, MDPI, vol. 9(1), pages 1-21, December.

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