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Abstract

In this study, the authors of the current work describe a novel exponentiated Weibull distribution that they have invented. The study was written by the writers of the current work. It is required to analyze those properties once the pertinent mathematical properties have been derived. In addition to the dispersion index, the anticipated value, variance, skewness, and kurtosis are also statistically examined. The dispersion index is likewise examined. Other beneficial shapes that the new density can assume include "bathtub," "right skewed," "bimodal and left skewed," "unimodal and left skewed," and "bimodal and right skewed." Additionally, these forms can be merged to create a "bathtub." The term "bathtub (U-HRF)," "constant," "monotonically increasing," "upside down-increasing (reversed U-increasing)," "J-HRF," "upside down-constant," "increasing-constant," or "upside down (reversed U)" may be used to describe the new rate of failure. The greatest likelihood method's efficiency is assessed via graphical analysis. The main measures for this procedure’s evaluation are biases and mean squared errors. The reader is given a scenario that graphically displays the adaptability and value of the innovative distribution through the use of three separate sets of actual data.

Keywords

Weibull Distribution Rényi entropy index Farlie Gumbel Morgenstern copula Real Data Modeling Hazard Function Clayton copula

Article Details

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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CC BY: This license allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator. The license allows for commercial use.

 

Author Biographies

Mahmoud Ali Selim, Applied College, King Khalid University, KSA

Department of Statistics, Faculty of Commerce, Al-Azhar University, Egypt.

Emadeldin I. A. Ali, Department of Economics, College of Economics and Administrative Sciences, Al Imam Mohammad Ibn Saud Islamic University, Saudi Arabia

Department of Mathematics, Statistics, and Insurance, Faculty of Business, Ain Shams University, Egypt

How to Cite
Refaie, M. K. A., Yaqoob, A. A., Selim, M. A., & Ali, E. I. A. (2023). A Novel Version of the Exponentiated Weibull Distribution: Copulas, Mathematical Properties and Statistical Modeling. Pakistan Journal of Statistics and Operation Research, 19(3), 491-519. https://doi.org/10.18187/pjsor.v19i3.4089
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