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Article

Statistical Inference on a Finite Mixture of Exponentiated Kumaraswamy-G Distributions with Progressive Type II Censoring Using Bladder Cancer Data

by
Refah Alotaibi
1,
Lamya A. Baharith
2,
Ehab M. Almetwally
3,4,5,
Mervat Khalifa
6,
Indranil Ghosh
7,* and
Hoda Rezk
6
1
Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, Riyadh 11671, Saudi Arabia
2
Department of Statistics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
3
Department of Statistical, Faculty of Business Administration, Delta University for Science and Technology, Gamasa 11152, Egypt
4
Department of Mathematical Statistical, Faculty of Graduate Studies for Statistical Research, Cairo University, Cairo 12613, Egypt
5
The Scientific Association for Studies and Applied Research, Al Manzalah 35646, Egypt
6
Department of Statistics, Al-Azhar University, Cairo 11751, Egypt
7
Department of Mathematics and Statistics, University of North Carolina, Wilmington, NC 27599, USA
*
Author to whom correspondence should be addressed.
Mathematics 2022, 10(15), 2800; https://doi.org/10.3390/math10152800
Submission received: 6 May 2022 / Revised: 18 July 2022 / Accepted: 19 July 2022 / Published: 7 August 2022
(This article belongs to the Special Issue New Advances in Distribution Theory and Its Applications)
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Abstract

A new family of distributions called the mixture of the exponentiated Kumaraswamy-G (henceforth, in short, ExpKum-G) class is developed. We consider Weibull distribution as the baseline (G) distribution to propose and study this special sub-model, which we call the exponentiated Kumaraswamy Weibull distribution. Several useful statistical properties of the proposed ExpKum-G distribution are derived. Under the classical paradigm, we consider the maximum likelihood estimation under progressive type II censoring to estimate the model parameters. Under the Bayesian paradigm, independent gamma priors are proposed to estimate the model parameters under progressive type II censored samples, assuming several loss functions. A simulation study is carried out to illustrate the efficiency of the proposed estimation strategies under both classical and Bayesian paradigms, based on progressively type II censoring models. For illustrative purposes, a real data set is considered that exhibits that the proposed model in the new class provides a better fit than other types of finite mixtures of exponentiated Kumaraswamy-type models.
Keywords: Kumaraswamy-G distribution; Bayesian approach; finite mixture; exponentiated Kumaraswamy Weibull distribution; loss function; progressive type II censoring Kumaraswamy-G distribution; Bayesian approach; finite mixture; exponentiated Kumaraswamy Weibull distribution; loss function; progressive type II censoring

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MDPI and ACS Style

Alotaibi, R.; Baharith, L.A.; Almetwally, E.M.; Khalifa, M.; Ghosh, I.; Rezk, H. Statistical Inference on a Finite Mixture of Exponentiated Kumaraswamy-G Distributions with Progressive Type II Censoring Using Bladder Cancer Data. Mathematics 2022, 10, 2800. https://doi.org/10.3390/math10152800

AMA Style

Alotaibi R, Baharith LA, Almetwally EM, Khalifa M, Ghosh I, Rezk H. Statistical Inference on a Finite Mixture of Exponentiated Kumaraswamy-G Distributions with Progressive Type II Censoring Using Bladder Cancer Data. Mathematics. 2022; 10(15):2800. https://doi.org/10.3390/math10152800

Chicago/Turabian Style

Alotaibi, Refah, Lamya A. Baharith, Ehab M. Almetwally, Mervat Khalifa, Indranil Ghosh, and Hoda Rezk. 2022. "Statistical Inference on a Finite Mixture of Exponentiated Kumaraswamy-G Distributions with Progressive Type II Censoring Using Bladder Cancer Data" Mathematics 10, no. 15: 2800. https://doi.org/10.3390/math10152800

APA Style

Alotaibi, R., Baharith, L. A., Almetwally, E. M., Khalifa, M., Ghosh, I., & Rezk, H. (2022). Statistical Inference on a Finite Mixture of Exponentiated Kumaraswamy-G Distributions with Progressive Type II Censoring Using Bladder Cancer Data. Mathematics, 10(15), 2800. https://doi.org/10.3390/math10152800

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