Open Access

ARTICLE

On a New Version of Weibull Model: Statistical Properties, Parameter Estimation and Applications

by Hassan Okasha^1,2, Mazen Nassar^1,3,*

1 Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia
2 Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Cairo, 11884, Egypt
3 Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig, 44519, Egypt

* Corresponding Authors: Mazen Nassar. Email: ;

Computer Modeling in Engineering & Sciences 2023, 137(3), 2219-2241. https://doi.org/10.32604/cmes.2023.028783

Received 07 January 2023; Accepted 05 May 2023; Issue published 03 August 2023

Abstract

In this paper, we introduce a new four-parameter version of the traditional Weibull distribution. It is able to provide seven shapes of hazard rate, including constant, decreasing, increasing, unimodal, bathtub, unimodal then bathtub, and bathtub then unimodal shapes. Some basic characteristics of the proposed model are studied, including moments, entropies, mean deviations and order statistics, and its parameters are estimated using the maximum likelihood approach. Based on the asymptotic properties of the estimators, the approximate confidence intervals are also taken into consideration in addition to the point estimators. We examine the effectiveness of the maximum likelihood estimators of the model’s parameters through simulation research. Based on the simulation findings, it can be concluded that the provided estimators are consistent and that asymptotic normality is a good method to get the interval estimates. Three actual data sets for COVID-19, engineering and blood cancer are used to empirically demonstrate the new distribution’s usefulness in modeling real-world data. The analysis demonstrates the proposed distribution’s ability in modeling many forms of data as opposed to some of its well-known sub-models, such as alpha power Weibull distribution.

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Keywords

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