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Statistical Inference on the Shannon and Rényi Entropy Measures of Generalized Exponential Distribution Under the Progressive Censoring

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Abstract

The aim of this paper is twofold. First, the estimation of the Shannon and Rényi entropy measures of a generalized exponential distribution is discussed when data are progressively censored. The maximum-likelihood estimates are obtained. The Bayes estimates with respect to three loss functions are proposed. It is assumed that the unknown parameters have independent gamma priors. The closed-form expressions of the Bayes estimates cannot be obtained. Therefore, Lindley’s approximation and importance sampling methods are employed. The asymptotic confidence intervals are computed. The normal approximation of the maximum-likelihood estimate and the log-transformed maximum-likelihood estimate are used. In addition, bootstrap algorithms are used to compute the confidence intervals. Highest posterior density credible intervals of the entropy functions are developed. A detailed numerical study is performed to compare the proposed estimates with respect to their average values and the mean squared errors. The confidence intervals are compared with respect to the average lengths. A real dataset is considered to illustrate the proposed methods. Furthermore, different criteria are proposed for the comparison of various sampling schemes. Then, the optimal sampling scheme for a given criterion is obtained.

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Acknowledgements

The authors like to thank the Editor-in-Chief, an associate editor, and anonymous referee for careful reading and useful comments, which have led this improved version. One of the authors, Kousik Maiti, thanks the financial support provided by the MHRD, Government of India. Suchandan Kayal gratefully acknowledges the partial financial support for this research work under a Grant MTR/2018/000350, SERB, India.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Rourkela, Rourkela, 769008, India

    Kousik Maiti & Suchandan Kayal

  2. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, 208016, India

    Debasis Kundu

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  1. Kousik Maiti
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  2. Suchandan Kayal
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  3. Debasis Kundu
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Correspondence to Suchandan Kayal.

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Maiti, K., Kayal, S. & Kundu, D. Statistical Inference on the Shannon and Rényi Entropy Measures of Generalized Exponential Distribution Under the Progressive Censoring. SN COMPUT. SCI. 3, 317 (2022). https://doi.org/10.1007/s42979-022-01200-2

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