{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T06:39:49Z","timestamp":1774593589689,"version":"3.50.1"},"reference-count":52,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,10,24]],"date-time":"2021-10-24T00:00:00Z","timestamp":1635033600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003482","name":"Department of Education of Hebei Province","doi-asserted-by":"publisher","award":["(ZD2018065)"],"award-info":[{"award-number":["(ZD2018065)"]}],"id":[{"id":"10.13039\/501100003482","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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 R\u00e9nyi 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.<\/jats:p>","DOI":"10.3390\/e23111394","type":"journal-article","created":{"date-parts":[[2021,10,24]],"date-time":"2021-10-24T22:06:16Z","timestamp":1635113176000},"page":"1394","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies"],"prefix":"10.3390","volume":"23","author":[{"given":"Mustapha","family":"Muhammad","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China"},{"name":"Department of Mathematical Sciences, Bayero University, Kano 700241, Nigeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5154-7477","authenticated-orcid":false,"given":"Huda M.","family":"Alshanbari","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5337-2276","authenticated-orcid":false,"given":"Ayed R. A.","family":"Alanzi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Human Studies at Hotat Sudair, Majmaah University, Majmaah 11952, Saudia Arabia"},{"name":"Department of Mathematics, College of Science and Arts in Gurayat, Jouf University, Gurayat 77454, Saudi Arabia"}]},{"given":"Lixia","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7948-1190","authenticated-orcid":false,"given":"Waqas","family":"Sami","sequence":"additional","affiliation":[{"name":"Department of Community Medicine & Public Health, College of Medicine, Majmaah University, Almajmaah 11952, Saudi Arabia"},{"name":"Azra Naheed Medical College, Superior University, Lahore 54000, Pakistan"}]},{"given":"Christophe","family":"Chesneau","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Caen-Normandie, 14032 Caen, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6192-9890","authenticated-orcid":false,"given":"Farrukh","family":"Jamal","sequence":"additional","affiliation":[{"name":"Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,24]]},"reference":[{"key":"ref_1","unstructured":"Evans, M., Hastings, N., and Peacock, B. 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