Bivariate power Lomax Sarmanov distribution: Statistical properties, Reliability measures, and Parameter estimation
This paper presents a bivariate power Lomax Sarmanov distribution (BPL-SARD) constructed from Sarmanov copulas and power Lomax (PL) marginal distributions. For modeling bivariate life expectancy data, this model provides a significant lifetime distribution. Several statistical properties of the BPL-...
Saved in:
| Main Authors: | , , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-02-01
|
| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824012419 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1825206954819059712 |
|---|---|
| author | M.A. Abd Elgawad M.A. Alawady H.M. Barakat G.M. Mansour I.A. Husseiny Salem A. Alyami Atef F. Hashem M.O. Mohamed |
| author_facet | M.A. Abd Elgawad M.A. Alawady H.M. Barakat G.M. Mansour I.A. Husseiny Salem A. Alyami Atef F. Hashem M.O. Mohamed |
| author_sort | M.A. Abd Elgawad |
| collection | DOAJ |
| description | This paper presents a bivariate power Lomax Sarmanov distribution (BPL-SARD) constructed from Sarmanov copulas and power Lomax (PL) marginal distributions. For modeling bivariate life expectancy data, this model provides a significant lifetime distribution. Several statistical properties of the BPL-SARD are derived and discussed, such as marginal distributions, product moments, coefficients of correlation between the inner variables, conditional distributions, conditional expectations, moment-generating functions, and the positive quadrant dependence property. We also obtained reliability measures, such as survival function, hazard rate function, mean residual life function, and vitality function. Model parameters are estimated using the maximum likelihood (ML) and Bayesian methods. Moreover, we derive asymptotic confidence intervals for the parameter model. To assess the effectiveness of both ML and Bayesian estimators, Monte Carlo simulation analysis is used. Furthermore, bootstrap confidence intervals were computed. Finally, two real data sets are analyzed to demonstrate the practical application of the proposed model. Because the Sarmanov copula is completely superior to all copulas that generalize the FGM copula, the BPL-SARD distribution performs better than any other bivariate PL distribution based on the FGM copula and its generalizations, which is the uniqueness and significance of this research. |
| format | Article |
| id | doaj-art-780ee4a967464ed98dd0fc12ed0f428c |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-780ee4a967464ed98dd0fc12ed0f428c2025-02-07T04:46:56ZengElsevierAlexandria Engineering Journal1110-01682025-02-01113593610Bivariate power Lomax Sarmanov distribution: Statistical properties, Reliability measures, and Parameter estimationM.A. Abd Elgawad0M.A. Alawady1H.M. Barakat2G.M. Mansour3I.A. Husseiny4Salem A. Alyami5Atef F. Hashem6M.O. Mohamed7Department of Mathematics and Statistics, Faculty of Science Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia; Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt; Corresponding author at: Department of Mathematics and Statistics, Faculty of Science Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia.Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, EgyptDepartment of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, EgyptDepartment of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, EgyptDepartment of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, EgyptDepartment of Mathematics and Statistics, Faculty of Science Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi ArabiaDepartment of Mathematics and Statistics, Faculty of Science Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia; Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62511, EgyptDepartment of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, EgyptThis paper presents a bivariate power Lomax Sarmanov distribution (BPL-SARD) constructed from Sarmanov copulas and power Lomax (PL) marginal distributions. For modeling bivariate life expectancy data, this model provides a significant lifetime distribution. Several statistical properties of the BPL-SARD are derived and discussed, such as marginal distributions, product moments, coefficients of correlation between the inner variables, conditional distributions, conditional expectations, moment-generating functions, and the positive quadrant dependence property. We also obtained reliability measures, such as survival function, hazard rate function, mean residual life function, and vitality function. Model parameters are estimated using the maximum likelihood (ML) and Bayesian methods. Moreover, we derive asymptotic confidence intervals for the parameter model. To assess the effectiveness of both ML and Bayesian estimators, Monte Carlo simulation analysis is used. Furthermore, bootstrap confidence intervals were computed. Finally, two real data sets are analyzed to demonstrate the practical application of the proposed model. Because the Sarmanov copula is completely superior to all copulas that generalize the FGM copula, the BPL-SARD distribution performs better than any other bivariate PL distribution based on the FGM copula and its generalizations, which is the uniqueness and significance of this research.http://www.sciencedirect.com/science/article/pii/S1110016824012419Sarmanov copulaLomax family of distributionsMaximum likelihood estimationBayesian estimationConfidence intervalsBootstrap |
| spellingShingle | M.A. Abd Elgawad M.A. Alawady H.M. Barakat G.M. Mansour I.A. Husseiny Salem A. Alyami Atef F. Hashem M.O. Mohamed Bivariate power Lomax Sarmanov distribution: Statistical properties, Reliability measures, and Parameter estimation Alexandria Engineering Journal Sarmanov copula Lomax family of distributions Maximum likelihood estimation Bayesian estimation Confidence intervals Bootstrap |
| title | Bivariate power Lomax Sarmanov distribution: Statistical properties, Reliability measures, and Parameter estimation |
| title_full | Bivariate power Lomax Sarmanov distribution: Statistical properties, Reliability measures, and Parameter estimation |
| title_fullStr | Bivariate power Lomax Sarmanov distribution: Statistical properties, Reliability measures, and Parameter estimation |
| title_full_unstemmed | Bivariate power Lomax Sarmanov distribution: Statistical properties, Reliability measures, and Parameter estimation |
| title_short | Bivariate power Lomax Sarmanov distribution: Statistical properties, Reliability measures, and Parameter estimation |
| title_sort | bivariate power lomax sarmanov distribution statistical properties reliability measures and parameter estimation |
| topic | Sarmanov copula Lomax family of distributions Maximum likelihood estimation Bayesian estimation Confidence intervals Bootstrap |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824012419 |
| work_keys_str_mv | AT maabdelgawad bivariatepowerlomaxsarmanovdistributionstatisticalpropertiesreliabilitymeasuresandparameterestimation AT maalawady bivariatepowerlomaxsarmanovdistributionstatisticalpropertiesreliabilitymeasuresandparameterestimation AT hmbarakat bivariatepowerlomaxsarmanovdistributionstatisticalpropertiesreliabilitymeasuresandparameterestimation AT gmmansour bivariatepowerlomaxsarmanovdistributionstatisticalpropertiesreliabilitymeasuresandparameterestimation AT iahusseiny bivariatepowerlomaxsarmanovdistributionstatisticalpropertiesreliabilitymeasuresandparameterestimation AT salemaalyami bivariatepowerlomaxsarmanovdistributionstatisticalpropertiesreliabilitymeasuresandparameterestimation AT ateffhashem bivariatepowerlomaxsarmanovdistributionstatisticalpropertiesreliabilitymeasuresandparameterestimation AT momohamed bivariatepowerlomaxsarmanovdistributionstatisticalpropertiesreliabilitymeasuresandparameterestimation |