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A Generalization of the Bivariate Gamma Distribution Based on Generalized Hypergeometric Functions

Author

Listed:
  • Christian Caamaño-Carrillo

    (Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, Chile)

  • Javier E. Contreras-Reyes

    (Instituto de Estadística, Facultad de Ciencias, Universidad de Valparaíso, Valparaíso 2360102, Chile)

Abstract

In this paper, we provide a new bivariate distribution obtained from a Kibble-type bivariate gamma distribution. The stochastic representation was obtained by the sum of a Kibble-type bivariate random vector and a bivariate random vector builded by two independent gamma random variables. In addition, the resulting bivariate density considers an infinite series of products of two confluent hypergeometric functions. In particular, we derive the probability and cumulative distribution functions, the moment generation and characteristic functions, the Hazard, Bonferroni and Lorenz functions, and an approximation for the differential entropy and mutual information index. Numerical examples showed the behavior of exact and approximated expressions.

Suggested Citation

  • Christian Caamaño-Carrillo & Javier E. Contreras-Reyes, 2022. "A Generalization of the Bivariate Gamma Distribution Based on Generalized Hypergeometric Functions," Mathematics, MDPI, vol. 10(9), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1502-:d:807065
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    References listed on IDEAS

    as
    1. A. Bekker & M. Arashi & J. T. Ferreira, 2019. "New bivariate gamma types with MIMO application," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(3), pages 596-615, February.
    2. Reinaldo B. Arellano-Valle & Javier E. Contreras-Reyes & Marc G. Genton, 2013. "Shannon Entropy and Mutual Information for Multivariate Skew-Elliptical Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(1), pages 42-62, March.
    3. Moreno Bevilacqua & Christian Caamaño‐Carrillo & Carlo Gaetan, 2020. "On modeling positive continuous data with spatiotemporal dependence," Environmetrics, John Wiley & Sons, Ltd., vol. 31(7), November.
    4. Contreras-Reyes, Javier E., 2014. "Asymptotic form of the Kullback–Leibler divergence for multivariate asymmetric heavy-tailed distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 200-208.
    5. Christian Caamaño-Carrillo & Javier E. Contreras-Reyes & Manuel González-Navarrete & Ewin Sánchez, 2020. "Bivariate superstatistics based on generalized gamma distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(3), pages 1-7, March.
    6. A. Mathal & P. Moschopoulos, 1992. "A form of multivariate gamma distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(1), pages 97-106, March.
    Full references (including those not matched with items on IDEAS)

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