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Multivariate Classes of GB2 Distributions with Applications

Author

Listed:
  • José María Sarabia

    (Department of Quantitative Methods, CUNEF University, Leonardo Prieto Castro 2, 28040 Madrid, Spain
    These authors contributed equally to this work.)

  • Vanesa Jordá

    (Department of Economics, University of Cantabria, Avda. de los Castros s/n, 39005 Santander, Spain
    These authors contributed equally to this work.)

  • Faustino Prieto

    (Department of Economics, University of Cantabria, Avda. de los Castros s/n, 39005 Santander, Spain
    These authors contributed equally to this work.)

  • Montserrat Guillén

    (Department of Econometrics, Riskcenter-IREA, University of Barcelona, Av. Diagonal, 690, 08034 Barcelona, Spain
    These authors contributed equally to this work.)

Abstract

The general beta of the second kind distribution (GB2) is a flexible distribution which includes several relevant parametric families of distributions. This distribution has important applications in earnings and income distributions, finance and insurance. In this paper, several multivariate classes of the GB2 distribution are proposed. The different multivariate versions are based on two simple univariate representations of the GB2 distribution. The first type of multivariate distributions are constructed from a stochastic dependent representations defined in terms of gamma random variables. Using this representation and beginning by two particular multivariate GB2 distributions, multivariate Singh–Maddala and Dagum income distributions are presented and several properties are obtained. Then, a general multivariate GB2 distribution is introduced. The second type of multivariate distributions are based on a generalization of the distribution of the order statistics, which gives place to multivariate GB2 distribution with support above the diagonal. We discuss the role of these families in modeling bivariate income distributions. Finally, an empirical application is given, where we show that a multivariate GB2 distribution can be useful for modeling compound precipitation and wind events in the whole range.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:72-:d:472831
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