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A New Three-Parameter Inverse Weibull Distribution with Medical and Engineering Applications

Refah Alotaibi1, Hassan Okasha2,3, Hoda Rezk4, Mazen Nassar2,5,*

1 Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh, 11671, Saudi Arabia
2 Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia
3 Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, 11884, Cairo, Egypt
4 Department of Statistics, Faculty of Commerce, Al-Azhar University, Nasr City, 11884, Cairo, Egypt
5 Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig, 44519, Egypt

* Corresponding Authors: Mazen Nassar. Email: ,

(This article belongs to this Special Issue: New Trends in Statistical Computing and Data Science)

Computer Modeling in Engineering & Sciences 2023, 135(2), 1255-1274.


The objective of this article is to provide a novel extension of the conventional inverse Weibull distribution that adds an extra shape parameter to increase its flexibility. This addition is beneficial in a variety of fields, including reliability, economics, engineering, biomedical science, biological research, environmental studies, and finance. For modeling real data, several expanded classes of distributions have been established. The modified alpha power transformed approach is used to implement the new model. The data matches the new inverse Weibull distribution better than the inverse Weibull distribution and several other competing models. It appears to be a distribution designed to support decreasing or unimodal shaped distributions based on its parameters. Precise expressions for quantiles, moments, incomplete moments, moment generating function, characteristic generating function, and entropy expression are among the determined attributes of the new distribution. The point and interval estimates are studied using the maximum likelihood method. Simulation research is conducted to illustrate the correctness of the theoretical results. Three applications to medical and engineering data are utilized to illustrate the model’s flexibility.


Cite This Article

Alotaibi, R., Okasha, H., Rezk, H., Nassar, M. (2023). A New Three-Parameter Inverse Weibull Distribution with Medical and Engineering Applications. CMES-Computer Modeling in Engineering & Sciences, 135(2), 1255–1274.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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