On a Bivariate Poisson Negative Binomial Risk Process
In this paper we define a bivariate counting process as a compound Poisson process with bivariate negative binomial compounding distribution. We investigate some of its basic properties, recursion formulas and probability mass function. Then we consider a risk model in which the claim counting proce...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Bulgarian Academy of Sciences, Institute of Mathematics and Informatics
2014-06-01
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| Series: | Biomath |
| Online Access: | http://www.biomathforum.org/biomath/index.php/biomath/article/view/232 |
| _version_ | 1797721115302297600 |
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| author | Krasimira Kostadinova Leda Minkova |
| author_facet | Krasimira Kostadinova Leda Minkova |
| author_sort | Krasimira Kostadinova |
| collection | DOAJ |
| description | In this paper we define a bivariate counting process as a compound Poisson process with bivariate negative binomial compounding distribution. We investigate some of its basic properties, recursion formulas and probability mass function. Then we consider a risk model in which the claim counting process is the defined bivariate Poisson negative binomial process. For the defined risk model we derive the distribution of the time to ruin in two cases and the corresponding Laplace transforms. We discuss in detail the particular case of exponentially distributed claims. |
| first_indexed | 2024-03-12T09:29:51Z |
| format | Article |
| id | doaj.art-2e7f8be6dbea4a4cae85a8eaca284252 |
| institution | Directory Open Access Journal |
| issn | 1314-684X 1314-7218 |
| language | English |
| last_indexed | 2024-03-12T09:29:51Z |
| publishDate | 2014-06-01 |
| publisher | Bulgarian Academy of Sciences, Institute of Mathematics and Informatics |
| record_format | Article |
| series | Biomath |
| spelling | doaj.art-2e7f8be6dbea4a4cae85a8eaca2842522023-09-02T13:55:34ZengBulgarian Academy of Sciences, Institute of Mathematics and InformaticsBiomath1314-684X1314-72182014-06-013110.11145/j.biomath.2014.04.211236On a Bivariate Poisson Negative Binomial Risk ProcessKrasimira KostadinovaLeda MinkovaIn this paper we define a bivariate counting process as a compound Poisson process with bivariate negative binomial compounding distribution. We investigate some of its basic properties, recursion formulas and probability mass function. Then we consider a risk model in which the claim counting process is the defined bivariate Poisson negative binomial process. For the defined risk model we derive the distribution of the time to ruin in two cases and the corresponding Laplace transforms. We discuss in detail the particular case of exponentially distributed claims.http://www.biomathforum.org/biomath/index.php/biomath/article/view/232 |
| spellingShingle | Krasimira Kostadinova Leda Minkova On a Bivariate Poisson Negative Binomial Risk Process Biomath |
| title | On a Bivariate Poisson Negative Binomial Risk Process |
| title_full | On a Bivariate Poisson Negative Binomial Risk Process |
| title_fullStr | On a Bivariate Poisson Negative Binomial Risk Process |
| title_full_unstemmed | On a Bivariate Poisson Negative Binomial Risk Process |
| title_short | On a Bivariate Poisson Negative Binomial Risk Process |
| title_sort | on a bivariate poisson negative binomial risk process |
| url | http://www.biomathforum.org/biomath/index.php/biomath/article/view/232 |
| work_keys_str_mv | AT krasimirakostadinova onabivariatepoissonnegativebinomialriskprocess AT ledaminkova onabivariatepoissonnegativebinomialriskprocess |