Inverted Length-Biased Exponential Model: Statistical Inference and Modeling
This research article proposes a new probability distribution, referred to as the inverted length-biased exponential distribution. The hazard rate function (HZRF) and density function (PDF) in the new distribution allow additional flexibility as well as some desired features. It provides a more flex...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/1980480 |
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| author | Waleed Almutiry |
| author_facet | Waleed Almutiry |
| author_sort | Waleed Almutiry |
| collection | DOAJ |
| description | This research article proposes a new probability distribution, referred to as the inverted length-biased exponential distribution. The hazard rate function (HZRF) and density function (PDF) in the new distribution allow additional flexibility as well as some desired features. It provides a more flexible approach that may be used to represent many forms of real-world data. The quantile function (QuF), moments (MOs), moment generating function (MOGF), mean residual lifespan (MRLS), mean inactivity time (MINT), and probability weighted moments (PRWMOs) are among the mathematical and statistical features of the inverted length-biased exponential distribution. In the case of complete and type II censored samples (TIICS), the maximum likelihood (MLL) strategy can be used to estimate the model parameters. An asymptotic confidence interval (COI) of parameter is constructed at two confidence levels. We perform simulation study to examine the accuracy of estimates depending upon some statistical measures. Simulation results show that there is great agreement between theoretical and empirical studies. We demonstrate the new model’s relevance and adaptability by modeling three lifespan datasets. The proposed model is a better fit than the half logistic inverse Rayleigh (HLOIR), type II Topp–Leone inverse Rayleigh (TIITOLIR), and transmuted inverse Rayleigh (TRIR) distributions. We anticipate that the expanded distribution will attract a broader range of applications in a variety of fields of research. |
| format | Article |
| id | doaj-art-2b9670163bb94390a6d7c6f5295b2638 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-2b9670163bb94390a6d7c6f5295b26382025-02-03T01:26:25ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/19804801980480Inverted Length-Biased Exponential Model: Statistical Inference and ModelingWaleed Almutiry0Department of MathematicsThis research article proposes a new probability distribution, referred to as the inverted length-biased exponential distribution. The hazard rate function (HZRF) and density function (PDF) in the new distribution allow additional flexibility as well as some desired features. It provides a more flexible approach that may be used to represent many forms of real-world data. The quantile function (QuF), moments (MOs), moment generating function (MOGF), mean residual lifespan (MRLS), mean inactivity time (MINT), and probability weighted moments (PRWMOs) are among the mathematical and statistical features of the inverted length-biased exponential distribution. In the case of complete and type II censored samples (TIICS), the maximum likelihood (MLL) strategy can be used to estimate the model parameters. An asymptotic confidence interval (COI) of parameter is constructed at two confidence levels. We perform simulation study to examine the accuracy of estimates depending upon some statistical measures. Simulation results show that there is great agreement between theoretical and empirical studies. We demonstrate the new model’s relevance and adaptability by modeling three lifespan datasets. The proposed model is a better fit than the half logistic inverse Rayleigh (HLOIR), type II Topp–Leone inverse Rayleigh (TIITOLIR), and transmuted inverse Rayleigh (TRIR) distributions. We anticipate that the expanded distribution will attract a broader range of applications in a variety of fields of research.http://dx.doi.org/10.1155/2021/1980480 |
| spellingShingle | Waleed Almutiry Inverted Length-Biased Exponential Model: Statistical Inference and Modeling Journal of Mathematics |
| title | Inverted Length-Biased Exponential Model: Statistical Inference and Modeling |
| title_full | Inverted Length-Biased Exponential Model: Statistical Inference and Modeling |
| title_fullStr | Inverted Length-Biased Exponential Model: Statistical Inference and Modeling |
| title_full_unstemmed | Inverted Length-Biased Exponential Model: Statistical Inference and Modeling |
| title_short | Inverted Length-Biased Exponential Model: Statistical Inference and Modeling |
| title_sort | inverted length biased exponential model statistical inference and modeling |
| url | http://dx.doi.org/10.1155/2021/1980480 |
| work_keys_str_mv | AT waleedalmutiry invertedlengthbiasedexponentialmodelstatisticalinferenceandmodeling |