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Estimation of the Generalized Logarithmic Transformation Exponential Distribution under Progressively Type-II Censored Data with Application to the COVID-19 Mortality Rates

Author

Listed:
  • Olayan Albalawi

    (Department of Statistics, Faculty of Science, University of Tabuk, Tabuk 47512, Saudi Arabia)

  • Naresh Chandra Kabdwal

    (Department of Mathematics and Statistics, Banasthali Vidyapith, Vanasthali 304022, Rajasthan, India)

  • Qazi J. Azhad

    (Department of Mathematics and Statistics, Banasthali Vidyapith, Vanasthali 304022, Rajasthan, India)

  • Rashi Hora

    (Department of Mathematics and Statistics, Banasthali Vidyapith, Vanasthali 304022, Rajasthan, India)

  • Basim S. O. Alsaedi

    (Department of Statistics, Faculty of Science, University of Tabuk, Tabuk 47512, Saudi Arabia)

Abstract

In this paper, classical and Bayesian estimation for the parameters and the reliability function for the generalized logarithmic transformation exponential (GLTE) distribution has been proposed when the life-times are progressively censored. The maximum likelihood estimator of unknown parameters and their corresponding reliability function are obtained under the classical setup. The Bayes estimators are obtained for symmetric (squared error) and asymmetric (LINEX and general entropy) loss functions. This was achieved by considering discrete prior for the scale parameter and conditional gamma prior for the shape parameter. Interval estimation of the unknown parameters and reliability function for classical and Bayesian schemes is also considered. The performances of various derived estimators are recorded using simulation study for different sample sizes and progressive censoring schemes. Finally, the COVID-19 mortality data sets are provided to illustrate the computation of various estimators.

Suggested Citation

  • Olayan Albalawi & Naresh Chandra Kabdwal & Qazi J. Azhad & Rashi Hora & Basim S. O. Alsaedi, 2022. "Estimation of the Generalized Logarithmic Transformation Exponential Distribution under Progressively Type-II Censored Data with Application to the COVID-19 Mortality Rates," Mathematics, MDPI, vol. 10(7), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1015-:d:776708
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    References listed on IDEAS

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    1. N. Balakrishnan, 2007. "Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 211-259, August.
    2. N. Balakrishnan, 2007. "Rejoinder on: Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 290-296, August.
    3. Boikanyo Makubate & Fastel Chipepa & Broderick Oluyede & Peter O. Peter, 2021. "The Marshall-Olkin Half Logistic-G Family of Distributions With Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(2), pages 120-120, March.
    4. Chansoo Kim & Jinhyouk Jung & Younshik Chung, 2011. "Bayesian estimation for the exponentiated Weibull model under Type II progressive censoring," Statistical Papers, Springer, vol. 52(1), pages 53-70, February.
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