A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies
In this article, we propose the exponentiated sine-generated family of distributions. Some important properties are demonstrated, such as the series representation of the probability density function, quantile function, moments, stress-strength reliability, and Rényi entropy. A particular member, ca...
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| Format: | Article |
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MDPI AG
2021-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/11/1394 |
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| author | Mustapha Muhammad Huda M. Alshanbari Ayed R. A. Alanzi Lixia Liu Waqas Sami Christophe Chesneau Farrukh Jamal |
| author_facet | Mustapha Muhammad Huda M. Alshanbari Ayed R. A. Alanzi Lixia Liu Waqas Sami Christophe Chesneau Farrukh Jamal |
| author_sort | Mustapha Muhammad |
| collection | DOAJ |
| description | In this article, we propose the exponentiated sine-generated family of distributions. Some important properties are demonstrated, such as the series representation of the probability density function, quantile function, moments, stress-strength reliability, and Rényi entropy. A particular member, called the exponentiated sine Weibull distribution, is highlighted; we analyze its skewness and kurtosis, moments, quantile function, residual mean and reversed mean residual life functions, order statistics, and extreme value distributions. Maximum likelihood estimation and Bayes estimation under the square error loss function are considered. Simulation studies are used to assess the techniques, and their performance gives satisfactory results as discussed by the mean square error, confidence intervals, and coverage probabilities of the estimates. The stress-strength reliability parameter of the exponentiated sine Weibull model is derived and estimated by the maximum likelihood estimation method. Also, nonparametric bootstrap techniques are used to approximate the confidence interval of the reliability parameter. A simulation is conducted to examine the mean square error, standard deviations, confidence intervals, and coverage probabilities of the reliability parameter. Finally, three real applications of the exponentiated sine Weibull model are provided. One of them considers stress-strength data. |
| first_indexed | 2024-03-10T05:31:09Z |
| format | Article |
| id | doaj.art-0abb26cc3be6436c8a4c8a3b6af02de1 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T05:31:09Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-0abb26cc3be6436c8a4c8a3b6af02de12023-11-22T23:14:19ZengMDPI AGEntropy1099-43002021-10-012311139410.3390/e23111394A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime StudiesMustapha Muhammad0Huda M. Alshanbari1Ayed R. A. Alanzi2Lixia Liu3Waqas Sami4Christophe Chesneau5Farrukh Jamal6School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, ChinaDepartment of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Mathematics, College of Science and Human Studies at Hotat Sudair, Majmaah University, Majmaah 11952, Saudia ArabiaSchool of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, ChinaDepartment of Community Medicine & Public Health, College of Medicine, Majmaah University, Almajmaah 11952, Saudi ArabiaDepartment of Mathematics, University of Caen-Normandie, 14032 Caen, FranceDepartment of Statistics, The Islamia University of Bahawalpur, Punjab 63100, PakistanIn this article, we propose the exponentiated sine-generated family of distributions. Some important properties are demonstrated, such as the series representation of the probability density function, quantile function, moments, stress-strength reliability, and Rényi entropy. A particular member, called the exponentiated sine Weibull distribution, is highlighted; we analyze its skewness and kurtosis, moments, quantile function, residual mean and reversed mean residual life functions, order statistics, and extreme value distributions. Maximum likelihood estimation and Bayes estimation under the square error loss function are considered. Simulation studies are used to assess the techniques, and their performance gives satisfactory results as discussed by the mean square error, confidence intervals, and coverage probabilities of the estimates. The stress-strength reliability parameter of the exponentiated sine Weibull model is derived and estimated by the maximum likelihood estimation method. Also, nonparametric bootstrap techniques are used to approximate the confidence interval of the reliability parameter. A simulation is conducted to examine the mean square error, standard deviations, confidence intervals, and coverage probabilities of the reliability parameter. Finally, three real applications of the exponentiated sine Weibull model are provided. One of them considers stress-strength data.https://www.mdpi.com/1099-4300/23/11/1394sine-generated familyWeibull distributionquantileentropyparametric estimationBayes estimation |
| spellingShingle | Mustapha Muhammad Huda M. Alshanbari Ayed R. A. Alanzi Lixia Liu Waqas Sami Christophe Chesneau Farrukh Jamal A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies Entropy sine-generated family Weibull distribution quantile entropy parametric estimation Bayes estimation |
| title | A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies |
| title_full | A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies |
| title_fullStr | A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies |
| title_full_unstemmed | A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies |
| title_short | A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies |
| title_sort | new generator of probability models the exponentiated sine g family for lifetime studies |
| topic | sine-generated family Weibull distribution quantile entropy parametric estimation Bayes estimation |
| url | https://www.mdpi.com/1099-4300/23/11/1394 |
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