A Generalization of the Bivariate Gamma Distribution Based on Generalized Hypergeometric Functions
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/9/1502 |
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| author | Christian Caamaño-Carrillo Javier E. Contreras-Reyes |
| author_facet | Christian Caamaño-Carrillo Javier E. Contreras-Reyes |
| author_sort | Christian Caamaño-Carrillo |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T03:56:35Z |
| format | Article |
| id | doaj.art-664d48ac20b44e31872f21594403030a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:56:35Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-664d48ac20b44e31872f21594403030a2023-11-23T08:45:19ZengMDPI AGMathematics2227-73902022-05-01109150210.3390/math10091502A Generalization of the Bivariate Gamma Distribution Based on Generalized Hypergeometric FunctionsChristian Caamaño-Carrillo0Javier E. Contreras-Reyes1Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, ChileInstituto de Estadística, Facultad de Ciencias, Universidad de Valparaíso, Valparaíso 2360102, ChileIn 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.https://www.mdpi.com/2227-7390/10/9/1502generalized gamma distributiongeneralized hypergeometric functionmoment generation functiondifferential entropymutual information |
| spellingShingle | Christian Caamaño-Carrillo Javier E. Contreras-Reyes A Generalization of the Bivariate Gamma Distribution Based on Generalized Hypergeometric Functions Mathematics generalized gamma distribution generalized hypergeometric function moment generation function differential entropy mutual information |
| title | A Generalization of the Bivariate Gamma Distribution Based on Generalized Hypergeometric Functions |
| title_full | A Generalization of the Bivariate Gamma Distribution Based on Generalized Hypergeometric Functions |
| title_fullStr | A Generalization of the Bivariate Gamma Distribution Based on Generalized Hypergeometric Functions |
| title_full_unstemmed | A Generalization of the Bivariate Gamma Distribution Based on Generalized Hypergeometric Functions |
| title_short | A Generalization of the Bivariate Gamma Distribution Based on Generalized Hypergeometric Functions |
| title_sort | generalization of the bivariate gamma distribution based on generalized hypergeometric functions |
| topic | generalized gamma distribution generalized hypergeometric function moment generation function differential entropy mutual information |
| url | https://www.mdpi.com/2227-7390/10/9/1502 |
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