Statistical inference of entropy functions of generalized inverse exponential model under progressive type-II censoring test

• Published in: PloS one Vol. 19; no. 9; p. e0311129
• Main Authors: Gong, Qin, Yin, Bin
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 30.09.2024
• Subjects: Algorithms; Analysis; Bayes Theorem; Bayesian analysis; Censoring (Statistics); Computer and Information Sciences; Computer Simulation; Confidence intervals; Decision making; Entropy; Entropy (Information theory); Estimates; Estimation accuracy; Evaluation; Experiments; Generalized inverse; Humans; Hypotheses; Hypothesis testing; Information theory; Lifetime; Likelihood Functions; Maximum likelihood estimation; Models, Statistical; Parameter estimation; Performance evaluation; Physical Sciences; Probability distribution functions; Random variables; Reliability engineering; Research and analysis methods; Risk assessment; Statistical analysis; Statistical inference; Statistical methods; Statistical models; Survival analysis; Trends; China
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0311129

This article explores the estimation of Shannon entropy and Rényi entropy based on the generalized inverse exponential distribution under the condition of stepwise Type II truncated samples. Firstly, we analyze the maximum likelihood estimation and interval estimation of Shannon entropy and Rényi entropy for the generalized inverse exponential distribution. In this process, we use the bootstrap method to construct confidence intervals for Shannon entropy and Rényi entropy. Next, we select the gamma distribution as the prior distribution and apply the Lindley approximation algorithm to calculate `estimates of Shannon entropy and Rényi entropy under different loss functions including Linex loss function, entropy loss function, and DeGroot loss function respectively. Afterwards, simulation is used to calculate estimates and corresponding mean square errors of Shannon entropy and Rényi entropy in GIED model. The research results show that under DeGroot loss function, estimation accuracy of Shannon entropy and Rényi entropy for generalized inverse exponential distribution is relatively high, overall Bayesian estimation performs better than maximum likelihood estimation. Finally, we demonstrate effectiveness of our estimation method in practical applications using a set of real data.