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Statistical Inference on the Shannon Entropy of Inverse Weibull Distribution under the Progressive First-Failure Censoring

School of Science, Beijing Jiaotong University, Beijing 100044, China
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Entropy 2019, 21(12), 1209; https://doi.org/10.3390/e21121209
Received: 2 November 2019 / Revised: 30 November 2019 / Accepted: 4 December 2019 / Published: 10 December 2019
Entropy is an uncertainty measure of random variables which mathematically represents the prospective quantity of the information. In this paper, we mainly focus on the estimation for the parameters and entropy of an Inverse Weibull distribution under progressive first-failure censoring using classical (Maximum Likelihood) and Bayesian methods. For Bayesian approaches, the Bayesian estimates are obtained based on both asymmetric (General Entropy, Linex) and symmetric (Squared Error) loss functions. Due to the complex form of Bayes estimates, we cannot get an explicit solution. Therefore, the Lindley method as well as Importance Sampling procedure is applied. Furthermore, using Importance Sampling method, the Highest Posterior Density credible intervals of entropy are constructed. As a comparison, the asymptotic intervals of entropy are also gained. Finally, a simulation study is implemented and a real data set analysis is performed to apply the previous methods. View Full-Text
Keywords: inverse Weibull distribution; entropy; progressive first-failure censored sample; maximum likelihood estimation; asymptotic interval; Lindley method; importance sampling procedure; highest posterior density credible interval inverse Weibull distribution; entropy; progressive first-failure censored sample; maximum likelihood estimation; asymptotic interval; Lindley method; importance sampling procedure; highest posterior density credible interval
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Yu, J.; Gui, W.; Shan, Y. Statistical Inference on the Shannon Entropy of Inverse Weibull Distribution under the Progressive First-Failure Censoring. Entropy 2019, 21, 1209.

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