Cumulant-Based Goodness-of-Fit Tests for the Tweedie, Bar-Lev and Enis Class of Distributions
The class of natural exponential families (NEFs) of distributions having power variance functions (NEF-PVFs) is huge (uncountable), with enormous applications in various fields. Based on a characterization property that holds for the cumulants of the members of this class, we developed a novel goodn...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-03-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/7/1603 |
| _version_ | 1797607485126737920 |
|---|---|
| author | Shaul K. Bar-Lev Apostolos Batsidis Jochen Einbeck Xu Liu Panpan Ren |
| author_facet | Shaul K. Bar-Lev Apostolos Batsidis Jochen Einbeck Xu Liu Panpan Ren |
| author_sort | Shaul K. Bar-Lev |
| collection | DOAJ |
| description | The class of natural exponential families (NEFs) of distributions having power variance functions (NEF-PVFs) is huge (uncountable), with enormous applications in various fields. Based on a characterization property that holds for the cumulants of the members of this class, we developed a novel goodness-of-fit (gof) test for testing whether a given random sample fits fixed members of this class. We derived the asymptotic null distribution of the test statistic and developed an appropriate bootstrap scheme. As the content of the paper is mainly theoretical, we exemplify its applicability to only a few elements of the NEF-PVF class, specifically, the gamma and modified Bessel-type NEFs. A Monte Carlo study was executed for examining the performance of both—the asymptotic test and the bootstrap counterpart—in controlling the type I error rate and evaluating their power performance in the special case of gamma, while real data examples demonstrate the applicability of the gof test to the modified Bessel distribution. |
| first_indexed | 2024-03-11T05:30:35Z |
| format | Article |
| id | doaj.art-5052e535cbb245c9a26495e1bcb32bdf |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T05:30:35Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5052e535cbb245c9a26495e1bcb32bdf2023-11-17T17:07:59ZengMDPI AGMathematics2227-73902023-03-01117160310.3390/math11071603Cumulant-Based Goodness-of-Fit Tests for the Tweedie, Bar-Lev and Enis Class of DistributionsShaul K. Bar-Lev0Apostolos Batsidis1Jochen Einbeck2Xu Liu3Panpan Ren4Faculty of Industrial Engineering and Technology Management, Holon Institute of Technology, Holon 6810201, IsraelDepartment of Mathematics, University of Ioannina, 45110 Ioannina, GreeceDepartment of Mathematical Sciences and Research Methods Centre, Durham University, Durham DH13LE, UKSchool of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, ChinaSchool of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, ChinaThe class of natural exponential families (NEFs) of distributions having power variance functions (NEF-PVFs) is huge (uncountable), with enormous applications in various fields. Based on a characterization property that holds for the cumulants of the members of this class, we developed a novel goodness-of-fit (gof) test for testing whether a given random sample fits fixed members of this class. We derived the asymptotic null distribution of the test statistic and developed an appropriate bootstrap scheme. As the content of the paper is mainly theoretical, we exemplify its applicability to only a few elements of the NEF-PVF class, specifically, the gamma and modified Bessel-type NEFs. A Monte Carlo study was executed for examining the performance of both—the asymptotic test and the bootstrap counterpart—in controlling the type I error rate and evaluating their power performance in the special case of gamma, while real data examples demonstrate the applicability of the gof test to the modified Bessel distribution.https://www.mdpi.com/2227-7390/11/7/1603natural exponential familygoodness-of-fit testspower variance functionTweedie scaleMonte Carlo simulationasymptotic distribution |
| spellingShingle | Shaul K. Bar-Lev Apostolos Batsidis Jochen Einbeck Xu Liu Panpan Ren Cumulant-Based Goodness-of-Fit Tests for the Tweedie, Bar-Lev and Enis Class of Distributions Mathematics natural exponential family goodness-of-fit tests power variance function Tweedie scale Monte Carlo simulation asymptotic distribution |
| title | Cumulant-Based Goodness-of-Fit Tests for the Tweedie, Bar-Lev and Enis Class of Distributions |
| title_full | Cumulant-Based Goodness-of-Fit Tests for the Tweedie, Bar-Lev and Enis Class of Distributions |
| title_fullStr | Cumulant-Based Goodness-of-Fit Tests for the Tweedie, Bar-Lev and Enis Class of Distributions |
| title_full_unstemmed | Cumulant-Based Goodness-of-Fit Tests for the Tweedie, Bar-Lev and Enis Class of Distributions |
| title_short | Cumulant-Based Goodness-of-Fit Tests for the Tweedie, Bar-Lev and Enis Class of Distributions |
| title_sort | cumulant based goodness of fit tests for the tweedie bar lev and enis class of distributions |
| topic | natural exponential family goodness-of-fit tests power variance function Tweedie scale Monte Carlo simulation asymptotic distribution |
| url | https://www.mdpi.com/2227-7390/11/7/1603 |
| work_keys_str_mv | AT shaulkbarlev cumulantbasedgoodnessoffittestsforthetweediebarlevandenisclassofdistributions AT apostolosbatsidis cumulantbasedgoodnessoffittestsforthetweediebarlevandenisclassofdistributions AT jocheneinbeck cumulantbasedgoodnessoffittestsforthetweediebarlevandenisclassofdistributions AT xuliu cumulantbasedgoodnessoffittestsforthetweediebarlevandenisclassofdistributions AT panpanren cumulantbasedgoodnessoffittestsforthetweediebarlevandenisclassofdistributions |