Entropy Analysis of the Weibull Population Mean Distributions

Document Type : Original papers

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Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt.

Abstract

The Weibull population mean (WPM) distribution is a versatile tool for modeling a wide range of real-world phenomena, including equipment lifetimes, medical data, and financial risks. In this study, we calculated the Shannon and Rényi entropies of the WPM distributions to gain deeper insights into its information content and uncertainty. Numerical simulations and graphical visualizations provide insights into the impact of parameter variations on the entropy. The results of this study highlight the WPM distribution's potential for capturing complex data patterns and its suitability for various applications. Our findings reveal that increasing the shape parameter of the WPM distribution leads to a higher degree of uncertainty, as in- dictated by the increasing entropy values. This is particularly relevant for modeling data with extreme events, such as those encountered in reliability engineering and survival analysis. By understanding the entropy properties of the WPM distribution, we can make more informed decisions in various applications.

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