A New Asymmetric Modified Topp–Leone Distribution: Classical and Bayesian Estimations under Progressive Type-II Censored Data with Applications
In this article, a new modified asymmetric Topp–Leone distribution is created and developed from a theoretical and inferential point of view. It has the feature of extending the remarkable flexibility of a special one-shape-parameter lifetime distribution, known as the inverse Topp–Leone distributio...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/7/1396 |
| _version_ | 1797587393567522816 |
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| author | Mohammed Elgarhy Najwan Alsadat Amal S. Hassan Christophe Chesneau Alaa H. Abdel-Hamid |
| author_facet | Mohammed Elgarhy Najwan Alsadat Amal S. Hassan Christophe Chesneau Alaa H. Abdel-Hamid |
| author_sort | Mohammed Elgarhy |
| collection | DOAJ |
| description | In this article, a new modified asymmetric Topp–Leone distribution is created and developed from a theoretical and inferential point of view. It has the feature of extending the remarkable flexibility of a special one-shape-parameter lifetime distribution, known as the inverse Topp–Leone distribution, to the bounded interval <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>1</mn><mo>]</mo></mrow></semantics></math></inline-formula>. The probability density function of the proposed truncated distribution has the potential to be unimodal and right-skewed, with different levels of asymmetry. On the other hand, its hazard rate function can be increasingly shaped. Some important statistical properties are examined, including several different measures. In practice, the estimation of the model parameters under progressive type-II censoring is considered. To achieve this aim, the maximum likelihood, maximum product of spacings, and Bayesian approaches are used. The Markov chain Monte Carlo approach is employed to produce the Bayesian estimates under the squared error and linear exponential loss functions. Some simulation studies to evaluate these approaches are discussed. Two applications based on real-world datasets—one on the times of infection, and the second dataset is on trading economics credit rating—are considered. Thanks to its flexible asymmetric features, the new model is preferable to some known comparable models. |
| first_indexed | 2024-03-11T00:36:26Z |
| format | Article |
| id | doaj.art-ad00c8e6cb4d476ba16c39d324cd9840 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T00:36:26Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-ad00c8e6cb4d476ba16c39d324cd98402023-11-18T21:34:29ZengMDPI AGSymmetry2073-89942023-07-01157139610.3390/sym15071396A New Asymmetric Modified Topp–Leone Distribution: Classical and Bayesian Estimations under Progressive Type-II Censored Data with ApplicationsMohammed Elgarhy0Najwan Alsadat1Amal S. Hassan2Christophe Chesneau3Alaa H. Abdel-Hamid4Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62521, EgyptDepartment of Quantitative Analysis, College of Business Administration, King Saud University, P.O. Box 71115, Riyadh 11587, Saudi ArabiaFaculty of Graduate Studies for Statistical Research, Cairo University, 5 Dr. Ahmed Zewail Street, Giza 12613, EgyptDepartment of Mathematics, University de Caen Normandie, Campus II, Science 3, 14032 Caen, FranceMathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62521, EgyptIn this article, a new modified asymmetric Topp–Leone distribution is created and developed from a theoretical and inferential point of view. It has the feature of extending the remarkable flexibility of a special one-shape-parameter lifetime distribution, known as the inverse Topp–Leone distribution, to the bounded interval <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mo> </mo><mn>1</mn><mo>]</mo></mrow></semantics></math></inline-formula>. The probability density function of the proposed truncated distribution has the potential to be unimodal and right-skewed, with different levels of asymmetry. On the other hand, its hazard rate function can be increasingly shaped. Some important statistical properties are examined, including several different measures. In practice, the estimation of the model parameters under progressive type-II censoring is considered. To achieve this aim, the maximum likelihood, maximum product of spacings, and Bayesian approaches are used. The Markov chain Monte Carlo approach is employed to produce the Bayesian estimates under the squared error and linear exponential loss functions. Some simulation studies to evaluate these approaches are discussed. Two applications based on real-world datasets—one on the times of infection, and the second dataset is on trading economics credit rating—are considered. Thanks to its flexible asymmetric features, the new model is preferable to some known comparable models.https://www.mdpi.com/2073-8994/15/7/1396maximum likelihood and Bayesian estimationsinverse Topp–Leone distributionmaximum product spacing estimationMarkov chain Monte Carloentropy and extropyprogressive type-II censoring |
| spellingShingle | Mohammed Elgarhy Najwan Alsadat Amal S. Hassan Christophe Chesneau Alaa H. Abdel-Hamid A New Asymmetric Modified Topp–Leone Distribution: Classical and Bayesian Estimations under Progressive Type-II Censored Data with Applications Symmetry maximum likelihood and Bayesian estimations inverse Topp–Leone distribution maximum product spacing estimation Markov chain Monte Carlo entropy and extropy progressive type-II censoring |
| title | A New Asymmetric Modified Topp–Leone Distribution: Classical and Bayesian Estimations under Progressive Type-II Censored Data with Applications |
| title_full | A New Asymmetric Modified Topp–Leone Distribution: Classical and Bayesian Estimations under Progressive Type-II Censored Data with Applications |
| title_fullStr | A New Asymmetric Modified Topp–Leone Distribution: Classical and Bayesian Estimations under Progressive Type-II Censored Data with Applications |
| title_full_unstemmed | A New Asymmetric Modified Topp–Leone Distribution: Classical and Bayesian Estimations under Progressive Type-II Censored Data with Applications |
| title_short | A New Asymmetric Modified Topp–Leone Distribution: Classical and Bayesian Estimations under Progressive Type-II Censored Data with Applications |
| title_sort | new asymmetric modified topp leone distribution classical and bayesian estimations under progressive type ii censored data with applications |
| topic | maximum likelihood and Bayesian estimations inverse Topp–Leone distribution maximum product spacing estimation Markov chain Monte Carlo entropy and extropy progressive type-II censoring |
| url | https://www.mdpi.com/2073-8994/15/7/1396 |
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