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On Estimation of Shannon’s Entropy of Maxwell Distribution Based on Progressively First-Failure Censored Data

Author

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  • Kapil Kumar

    (Department of Statistics, Central University of Haryana, Mahendergarh 123031, India
    These authors contributed equally to this work.)

  • Indrajeet Kumar

    (Department of Statistics, Central University of South Bihar, Gaya 824236, India
    These authors contributed equally to this work.)

  • Hon Keung Tony Ng

    (Department of Mathematical Sciences, Bentley University, Waltham, MA 02452, USA
    These authors contributed equally to this work.)

Abstract

Shannon’s entropy is a fundamental concept in information theory that quantifies the uncertainty or information in a random variable or data set. This article addresses the estimation of Shannon’s entropy for the Maxwell lifetime model based on progressively first-failure-censored data from both classical and Bayesian points of view. In the classical perspective, the entropy is estimated using maximum likelihood estimation and bootstrap methods. For Bayesian estimation, two approximation techniques, including the Tierney-Kadane (T-K) approximation and the Markov Chain Monte Carlo (MCMC) method, are used to compute the Bayes estimate of Shannon’s entropy under the linear exponential (LINEX) loss function. We also obtained the highest posterior density (HPD) credible interval of Shannon’s entropy using the MCMC technique. A Monte Carlo simulation study is performed to investigate the performance of the estimation procedures and methodologies studied in this manuscript. A numerical example is used to illustrate the methodologies. This paper aims to provide practical values in applied statistics, especially in the areas of reliability and lifetime data analysis.

Suggested Citation

  • Kapil Kumar & Indrajeet Kumar & Hon Keung Tony Ng, 2024. "On Estimation of Shannon’s Entropy of Maxwell Distribution Based on Progressively First-Failure Censored Data," Stats, MDPI, vol. 7(1), pages 1-22, February.
    • Handle: RePEc:gam:jstats:v:7:y:2024:i:1:p:9-159:d:1335923
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    References listed on IDEAS

    as
    1. Wu, Shuo-Jye & Kus, Coskun, 2009. "On estimation based on progressive first-failure-censored sampling," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3659-3670, August.
    2. Kayal, Suchandan & Kumar, Somesh, 2013. "Estimation of the Shannon’s entropy of several shifted exponential populations," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1127-1135.
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