Multivariate Classes of GB2 Distributions with Applications
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 classe...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-12-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/9/1/72 |
| _version_ | 1797542911717408768 |
|---|---|
| author | José María Sarabia Vanesa Jordá Faustino Prieto Montserrat Guillén |
| author_facet | José María Sarabia Vanesa Jordá Faustino Prieto Montserrat Guillén |
| author_sort | José María Sarabia |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T13:37:15Z |
| format | Article |
| id | doaj.art-e2e886d5395d442d879d90fe9bc06c5f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T13:37:15Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e2e886d5395d442d879d90fe9bc06c5f2023-11-21T07:27:01ZengMDPI AGMathematics2227-73902020-12-01917210.3390/math9010072Multivariate Classes of GB2 Distributions with ApplicationsJosé María Sarabia0Vanesa Jordá1Faustino Prieto2Montserrat Guillén3Department of Quantitative Methods, CUNEF University, Leonardo Prieto Castro 2, 28040 Madrid, SpainDepartment of Economics, University of Cantabria, Avda. de los Castros s/n, 39005 Santander, SpainDepartment of Economics, University of Cantabria, Avda. de los Castros s/n, 39005 Santander, SpainDepartment of Econometrics, Riskcenter-IREA, University of Barcelona, Av. Diagonal, 690, 08034 Barcelona, SpainThe 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.https://www.mdpi.com/2227-7390/9/1/72generalized beta distribution of the second kindmultivariate reductionbivariate income distributioncompound climate events |
| spellingShingle | José María Sarabia Vanesa Jordá Faustino Prieto Montserrat Guillén Multivariate Classes of GB2 Distributions with Applications Mathematics generalized beta distribution of the second kind multivariate reduction bivariate income distribution compound climate events |
| title | Multivariate Classes of GB2 Distributions with Applications |
| title_full | Multivariate Classes of GB2 Distributions with Applications |
| title_fullStr | Multivariate Classes of GB2 Distributions with Applications |
| title_full_unstemmed | Multivariate Classes of GB2 Distributions with Applications |
| title_short | Multivariate Classes of GB2 Distributions with Applications |
| title_sort | multivariate classes of gb2 distributions with applications |
| topic | generalized beta distribution of the second kind multivariate reduction bivariate income distribution compound climate events |
| url | https://www.mdpi.com/2227-7390/9/1/72 |
| work_keys_str_mv | AT josemariasarabia multivariateclassesofgb2distributionswithapplications AT vanesajorda multivariateclassesofgb2distributionswithapplications AT faustinoprieto multivariateclassesofgb2distributionswithapplications AT montserratguillen multivariateclassesofgb2distributionswithapplications |