A New Modified Kumaraswamy Distribution: Actuarial Measures and Applications
In this paper, a new modified Kumaraswamy distribution is proposed, and some of its basic properties are presented, such as the mathematical expressions for the moments, probability weighted moments, order statistics, quantile function, reliability, and entropy measures. The parameter estimation is...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/4288286 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850171166603345920 |
|---|---|
| author | Ayed R. A. Alanzi M. Qaisar Rafique M. H. Tahir Waqas Sami Farrukh Jamal |
| author_facet | Ayed R. A. Alanzi M. Qaisar Rafique M. H. Tahir Waqas Sami Farrukh Jamal |
| author_sort | Ayed R. A. Alanzi |
| collection | DOAJ |
| description | In this paper, a new modified Kumaraswamy distribution is proposed, and some of its basic properties are presented, such as the mathematical expressions for the moments, probability weighted moments, order statistics, quantile function, reliability, and entropy measures. The parameter estimation is done via the maximum likelihood estimation method. In order to show the usefulness of the proposed model, some well-established actuarial measures such as value-at-risk, expected-shortfall, tail-value-at-risk, tail-variance, and tail-variance-premium are obtained. A simulation study is carried out to assess the performance of maximum likelihood estimates. The empirical analysis is carried out to show that our proposed model is better in performance as compared to other competitive models related to the extended Kumaraswamy model. Thus, insurance claim data and engineering related real-life data sets are considered to prove this claim. |
| format | Article |
| id | doaj-art-a3a569e176b34abaa0bbbcc0f2d56d5a |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-a3a569e176b34abaa0bbbcc0f2d56d5a2025-08-20T02:20:20ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/4288286A New Modified Kumaraswamy Distribution: Actuarial Measures and ApplicationsAyed R. A. Alanzi0M. Qaisar Rafique1M. H. Tahir2Waqas Sami3Farrukh Jamal4Department of MathematicsDepartment of StatisticsDepartment of StatisticsCollege of NursingDepartment of StatisticsIn this paper, a new modified Kumaraswamy distribution is proposed, and some of its basic properties are presented, such as the mathematical expressions for the moments, probability weighted moments, order statistics, quantile function, reliability, and entropy measures. The parameter estimation is done via the maximum likelihood estimation method. In order to show the usefulness of the proposed model, some well-established actuarial measures such as value-at-risk, expected-shortfall, tail-value-at-risk, tail-variance, and tail-variance-premium are obtained. A simulation study is carried out to assess the performance of maximum likelihood estimates. The empirical analysis is carried out to show that our proposed model is better in performance as compared to other competitive models related to the extended Kumaraswamy model. Thus, insurance claim data and engineering related real-life data sets are considered to prove this claim.http://dx.doi.org/10.1155/2022/4288286 |
| spellingShingle | Ayed R. A. Alanzi M. Qaisar Rafique M. H. Tahir Waqas Sami Farrukh Jamal A New Modified Kumaraswamy Distribution: Actuarial Measures and Applications Journal of Mathematics |
| title | A New Modified Kumaraswamy Distribution: Actuarial Measures and Applications |
| title_full | A New Modified Kumaraswamy Distribution: Actuarial Measures and Applications |
| title_fullStr | A New Modified Kumaraswamy Distribution: Actuarial Measures and Applications |
| title_full_unstemmed | A New Modified Kumaraswamy Distribution: Actuarial Measures and Applications |
| title_short | A New Modified Kumaraswamy Distribution: Actuarial Measures and Applications |
| title_sort | new modified kumaraswamy distribution actuarial measures and applications |
| url | http://dx.doi.org/10.1155/2022/4288286 |
| work_keys_str_mv | AT ayedraalanzi anewmodifiedkumaraswamydistributionactuarialmeasuresandapplications AT mqaisarrafique anewmodifiedkumaraswamydistributionactuarialmeasuresandapplications AT mhtahir anewmodifiedkumaraswamydistributionactuarialmeasuresandapplications AT waqassami anewmodifiedkumaraswamydistributionactuarialmeasuresandapplications AT farrukhjamal anewmodifiedkumaraswamydistributionactuarialmeasuresandapplications AT ayedraalanzi newmodifiedkumaraswamydistributionactuarialmeasuresandapplications AT mqaisarrafique newmodifiedkumaraswamydistributionactuarialmeasuresandapplications AT mhtahir newmodifiedkumaraswamydistributionactuarialmeasuresandapplications AT waqassami newmodifiedkumaraswamydistributionactuarialmeasuresandapplications AT farrukhjamal newmodifiedkumaraswamydistributionactuarialmeasuresandapplications |