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Statistical Inference on the Entropy Measures of Gamma Distribution under Progressive Censoring: EM and MCMC Algorithms

Author

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  • Essam A. Ahmed

    (Applied College, Taibah University, Al-Madinah Al-Munawwarah 41941, Saudi Arabia
    Department of Mathematics, Sohag University, Sohag 82524, Egypt)

  • Mahmoud El-Morshedy

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Laila A. Al-Essa

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Mohamed S. Eliwa

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    Department of Statistics and Operation Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia
    Department of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy)

Abstract

Studying the ages of mobile phones is considered one of the most important things in the recent period in the field of shopping and modern technology. In this paper, we will consider that the ages of these phones follow a gamma distribution under progressive first-failure (PFF) censoring. All of the unknown parameters, as well as Shannon and Rényi entropies, were estimated for this distribution. The maximum likelihood (ML) approach was utilized to generate point estimates for the target parameters based on the considered censoring strategy. The asymptotic confidence intervals of the ML estimators (MLEs) of the targeted parameters were produced using the normal approximation to ML and log-transformed ML. We employed the delta method to approximate the variances of the Shannon and Rényi functions to obtain their asymptotic confidence intervals. Additionally, all parameter estimates utilized in this study were determined using the successful expectation–maximization (EM) method. The Metropolis–Hastings (MH) algorithm was applied to construct the Bayes estimators and related highest posterior density (HPD) credible intervals under various loss functions. Further, the proposed methodologies were contrasted using Monte Carlo simulations. Finally, the radio transceiver dataset was analyzed to substantiate our results.

Suggested Citation

  • Essam A. Ahmed & Mahmoud El-Morshedy & Laila A. Al-Essa & Mohamed S. Eliwa, 2023. "Statistical Inference on the Entropy Measures of Gamma Distribution under Progressive Censoring: EM and MCMC Algorithms," Mathematics, MDPI, vol. 11(10), pages 1-30, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2298-:d:1147313
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    References listed on IDEAS

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    Cited by:

    1. José H. Dias Gonçalves & João J. Ferreira Gomes & Lihki Rubio & Filipe R. Ramos, 2023. "A Generalized Log Gamma Approach: Theoretical Contributions and an Application to Companies’ Life Expectancy," Mathematics, MDPI, vol. 11(23), pages 1-23, November.

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