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Bayesian Estimations of Shannon Entropy and Rényi Entropy of Inverse Weibull Distribution
Version 1
: Received: 12 May 2023 / Approved: 15 May 2023 / Online: 15 May 2023 (11:14:14 CEST)
A peer-reviewed article of this Preprint also exists.
Ren, H.; Hu, X. Bayesian Estimations of Shannon Entropy and Rényi Entropy of Inverse Weibull Distribution. Mathematics 2023, 11, 2483. Ren, H.; Hu, X. Bayesian Estimations of Shannon Entropy and Rényi Entropy of Inverse Weibull Distribution. Mathematics 2023, 11, 2483.
Abstract
In this paper, under the symmetric entropy and the scale squared error loss functions, we consider the maximum likelihood (ML) estimation and Bayesian estimation of the Shannon entropy and Rényi entropy of the two-parameter inverse Weibull distribution. In the ML estimation, the dichotomy is used to solve likelihood equation. In addition, the approximation confidence interval is given by the Delta method. Because the form of estimation results is more complex in the Bayesian estimation, the Lindley approximation method is used to achieve the numerical calculation. Finally, Monte Carlo simulations and a real data set are used to illustrate the results derived. By comparing the mean square error between the estimated value and the real value, it can be found that the performance of ML estimation of Shannon entropy is better than that of Bayesian estimation, and there is no significant difference between the performance of ML estimation of Rényi entropy and that of Bayesian estimation.
Keywords
Inverse Weibull distribution; symmetric entropy loss function; Rényi entropy; Bayesian estimation; Lindley approximation
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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