Open Access

ARTICLE

A Novel Modified Alpha Power Transformed Weibull Distribution and Its Engineering Applications

Refah Alotaibi¹, Hassan Okasha^2,3, Mazen Nassar^2,4, Ahmed Elshahhat^5,*
1 Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia
2 Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, 80200, Saudi Arabia
3 Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Cairo, 11884, Egypt
4 Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig, 44519, Egypt
5 Faculty of Technology and Development, Zagazig University, Zagazig, 44519, Egypt
* Corresponding Author: Ahmed Elshahhat. Email:
(This article belongs to this Special Issue: New Trends in Statistical Computing and Data Science)

Computer Modeling in Engineering & Sciences 2023, 135(3), 2065-2089. https://doi.org/10.32604/cmes.2023.023408

Received 24 April 2022; Accepted 11 July 2022; Issue published 23 November 2022

Abstract

This paper suggests a new modified version of the traditional Weibull distribution by adding a new shape parameter utilising the modified alpha power transformed technique. We refer to the new model as modified alpha power transformed Weibull distribution. The attractiveness and significance of the new distribution lie in its power to model monotone and non-monotone failure rate functions, which are quite familiar in environmental investigations. Its hazard rate function can be decreasing, increasing, bathtub and upside-down then bathtub shaped. Diverse structural properties of the proposed model are acquired including quantile function, moments, entropies, order statistics, residual life and reversed failure rate function. The parameters of the distribution were estimated using the maximum likelihood function. The maximum likelihood method is employed to estimate the model parameters and the approximate confidence intervals are also computed. Via a simulation study, the performance of the point and interval estimates are compared using different criteria. Employing real lifetime data sets, we verify that the offered model furnishes a better fit than some other lifetime models including Weibull, gamma and alpha power Weibull models.

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Keywords

Weibull distribution; modified alpha power transformation method; maximum likelihood; entropy; order statistics

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