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

Christian Caamaño-Carrillo and Javier E. Contreras-Reyes
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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

Mathematics, 2022, vol. 10, issue 9, 1-17

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.

Keywords: generalized gamma distribution; generalized hypergeometric function; moment generation function; differential entropy; mutual information (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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