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Entropy
Volume 23
Issue 11
10.3390/e23111394
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Article

A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies

by
Mustapha Muhammad
1,2,
Huda M. Alshanbari
3,
Ayed R. A. Alanzi
4,5,
Lixia Liu
1,*,
Waqas Sami
6,7,
Christophe Chesneau
8 and
Farrukh Jamal
9,*
1
School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China
2
Department of Mathematical Sciences, Bayero University, Kano 700241, Nigeria
3
Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
4
Department of Mathematics, College of Science and Human Studies at Hotat Sudair, Majmaah University, Majmaah 11952, Saudia Arabia
5
Department of Mathematics, College of Science and Arts in Gurayat, Jouf University, Gurayat 77454, Saudi Arabia
6
Department of Community Medicine & Public Health, College of Medicine, Majmaah University, Almajmaah 11952, Saudi Arabia
7
Azra Naheed Medical College, Superior University, Lahore 54000, Pakistan
8
Department of Mathematics, University of Caen-Normandie, 14032 Caen, France
9
Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan
*
Authors to whom correspondence should be addressed.
Entropy 2021, 23(11), 1394; https://doi.org/10.3390/e23111394
Submission received: 13 September 2021 / Revised: 12 October 2021 / Accepted: 15 October 2021 / Published: 24 October 2021
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Abstract

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.
Keywords: sine-generated family; Weibull distribution; quantile; entropy; parametric estimation; Bayes estimation; stress-strength reliability sine-generated family; Weibull distribution; quantile; entropy; parametric estimation; Bayes estimation; stress-strength reliability

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MDPI and ACS Style

Muhammad, M.; Alshanbari, H.M.; Alanzi, A.R.A.; Liu, L.; Sami, W.; Chesneau, C.; Jamal, F. A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies. Entropy 2021, 23, 1394. https://doi.org/10.3390/e23111394

AMA Style

Muhammad M, Alshanbari HM, Alanzi ARA, Liu L, Sami W, Chesneau C, Jamal F. A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies. Entropy. 2021; 23(11):1394. https://doi.org/10.3390/e23111394

Chicago/Turabian Style

Muhammad, Mustapha, Huda M. Alshanbari, Ayed R. A. Alanzi, Lixia Liu, Waqas Sami, Christophe Chesneau, and Farrukh Jamal. 2021. "A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies" Entropy 23, no. 11: 1394. https://doi.org/10.3390/e23111394

APA Style

Muhammad, M., Alshanbari, H. M., Alanzi, A. R. A., Liu, L., Sami, W., Chesneau, C., & Jamal, F. (2021). A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies. Entropy, 23(11), 1394. https://doi.org/10.3390/e23111394

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