Inverse Exponentiated Lomax Power Series Distribution: Model, Estimation, and Application
In this paper, we introduce the inverse exponentiated Lomax power series (IELoPS) class of distributions, obtained by compounding the inverse exponentiated Lomax and power series distributions. The IELoPS class contains some significant new flexible lifetime distributions that possess powerful physi...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/1998653 |
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| author | Amal S. Hassan Ehab M. Almetwally Samia C. Gamoura Ahmed S. M. Metwally |
| author_facet | Amal S. Hassan Ehab M. Almetwally Samia C. Gamoura Ahmed S. M. Metwally |
| author_sort | Amal S. Hassan |
| collection | DOAJ |
| description | In this paper, we introduce the inverse exponentiated Lomax power series (IELoPS) class of distributions, obtained by compounding the inverse exponentiated Lomax and power series distributions. The IELoPS class contains some significant new flexible lifetime distributions that possess powerful physical explications applied in areas like industrial and biological studies. The IELoPS class comprises the inverse Lomax power series as a new subclass as well as several new flexible compounded lifetime distributions. For the proposed class, some characteristics and properties are derived such as hazard rate function, limiting behavior, quantile function, Lorenz and Bonferroni curves, mean residual life, mean inactivity time, and some measures of information. The methods of maximum likelihood and Bayesian estimations are used to estimate the model parameters of one optional model. The Bayesian estimators of parameters are discussed under squared error and linear exponential loss functions. The asymptotic confidence intervals, as well as Bayesian credible intervals, of parameters, are constructed. Simulations for a one-selective model, say inverse exponentiated Lomax Poisson (IELoP) distribution, are designed to assess and compare different estimates. Results of the study emphasized the merit of produced estimates. In addition, they appeared the superiority of Bayesian estimate under regarded priors compared to the corresponding maximum likelihood estimate. Finally, we examine medical and reliability data to demonstrate the applicability, flexibility, and usefulness of IELoP distribution. For the suggested two real data sets, the IELoP distribution fits better than Kumaraswamy–Weibull, Poisson–Lomax, Poisson inverse Lomax, Weibull–Lomax, Gumbel–Lomax, odd Burr–Weibull–Poisson, and power Lomax–Poisson distributions. |
| format | Article |
| id | doaj-art-936e2f2afb304274bb5add73043e5065 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-936e2f2afb304274bb5add73043e50652025-02-03T05:57:27ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/1998653Inverse Exponentiated Lomax Power Series Distribution: Model, Estimation, and ApplicationAmal S. Hassan0Ehab M. Almetwally1Samia C. Gamoura2Ahmed S. M. Metwally3Faculty of Graduate Studies for Statistical ResearchFaculty of Graduate Studies for Statistical ResearchStrasbourg UniversityDepartment of MathematicsIn this paper, we introduce the inverse exponentiated Lomax power series (IELoPS) class of distributions, obtained by compounding the inverse exponentiated Lomax and power series distributions. The IELoPS class contains some significant new flexible lifetime distributions that possess powerful physical explications applied in areas like industrial and biological studies. The IELoPS class comprises the inverse Lomax power series as a new subclass as well as several new flexible compounded lifetime distributions. For the proposed class, some characteristics and properties are derived such as hazard rate function, limiting behavior, quantile function, Lorenz and Bonferroni curves, mean residual life, mean inactivity time, and some measures of information. The methods of maximum likelihood and Bayesian estimations are used to estimate the model parameters of one optional model. The Bayesian estimators of parameters are discussed under squared error and linear exponential loss functions. The asymptotic confidence intervals, as well as Bayesian credible intervals, of parameters, are constructed. Simulations for a one-selective model, say inverse exponentiated Lomax Poisson (IELoP) distribution, are designed to assess and compare different estimates. Results of the study emphasized the merit of produced estimates. In addition, they appeared the superiority of Bayesian estimate under regarded priors compared to the corresponding maximum likelihood estimate. Finally, we examine medical and reliability data to demonstrate the applicability, flexibility, and usefulness of IELoP distribution. For the suggested two real data sets, the IELoP distribution fits better than Kumaraswamy–Weibull, Poisson–Lomax, Poisson inverse Lomax, Weibull–Lomax, Gumbel–Lomax, odd Burr–Weibull–Poisson, and power Lomax–Poisson distributions.http://dx.doi.org/10.1155/2022/1998653 |
| spellingShingle | Amal S. Hassan Ehab M. Almetwally Samia C. Gamoura Ahmed S. M. Metwally Inverse Exponentiated Lomax Power Series Distribution: Model, Estimation, and Application Journal of Mathematics |
| title | Inverse Exponentiated Lomax Power Series Distribution: Model, Estimation, and Application |
| title_full | Inverse Exponentiated Lomax Power Series Distribution: Model, Estimation, and Application |
| title_fullStr | Inverse Exponentiated Lomax Power Series Distribution: Model, Estimation, and Application |
| title_full_unstemmed | Inverse Exponentiated Lomax Power Series Distribution: Model, Estimation, and Application |
| title_short | Inverse Exponentiated Lomax Power Series Distribution: Model, Estimation, and Application |
| title_sort | inverse exponentiated lomax power series distribution model estimation and application |
| url | http://dx.doi.org/10.1155/2022/1998653 |
| work_keys_str_mv | AT amalshassan inverseexponentiatedlomaxpowerseriesdistributionmodelestimationandapplication AT ehabmalmetwally inverseexponentiatedlomaxpowerseriesdistributionmodelestimationandapplication AT samiacgamoura inverseexponentiatedlomaxpowerseriesdistributionmodelestimationandapplication AT ahmedsmmetwally inverseexponentiatedlomaxpowerseriesdistributionmodelestimationandapplication |