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Analysis of progressive type-II censored gamma distribution

Author

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  • Sanku Dey

    (St. Anthony’s College)

  • Ahmed Elshahhat

    (Zagazig University)

  • Mazen Nassar

    (King Abdulaziz University
    Zagazig University)

Abstract

The aim of this study is to describe the both frequentist and Bayesian parametric estimation methods for the gamma distribution using progressive Type II censoring data. We first take into account, maximum likelihood method and its competitive method, known as the maximum product of spacing method for estimation of parameters of the model. In addition, approximate confidence intervals based on asymptotic theory have been considered for both the methods. Further, based on flexible gamma priors for the shape and scale parameters, Bayes estimators under the assumption of squared error loss function are obtained using likelihood and maximum product of spacing functions, and also the associated highest posterior density credible intervals of the parameters are obtained. Monte-Carlo simulations are carried out to examine the performance of the proposed estimates using various criteria. We further present an optimal progressive censoring plan among different competing censoring plans using three optimality criteria. Finally, to show the applicability of the proposed methodologies in a real-life situation, one engineering data set and a clinical data set are investigated. The numerical results confirm that our proposed methods work satisfactorily.

Suggested Citation

  • Sanku Dey & Ahmed Elshahhat & Mazen Nassar, 2023. "Analysis of progressive type-II censored gamma distribution," Computational Statistics, Springer, vol. 38(1), pages 481-508, March.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:1:d:10.1007_s00180-022-01239-y
    DOI: 10.1007/s00180-022-01239-y
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    References listed on IDEAS

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    1. Sanku Dey & Mazen Nassar, 2020. "Classical methods of estimation on constant stress accelerated life tests under exponentiated Lindley distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(6), pages 975-996, April.
    2. Ahmed Elshahhat & Mazen Nassar, 2021. "Bayesian survival analysis for adaptive Type-II progressive hybrid censored Hjorth data," Computational Statistics, Springer, vol. 36(3), pages 1965-1990, September.
    3. Anatolyev, Stanislav & Kosenok, Grigory, 2005. "An Alternative To Maximum Likelihood Based On Spacings," Econometric Theory, Cambridge University Press, vol. 21(2), pages 472-476, April.
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    5. Hideki Nagatsuka & N. Balakrishnan & Toshinari Kamakura, 2014. "A Consistent Method of Estimation For The Three-Parameter Gamma Distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(18), pages 3905-3926, September.
    6. Abdullah M. Almarashi & Muhammad Aslam & Sami Ullah Khan, 2021. "Process Monitoring for Gamma Distributed Product under Neutrosophic Statistics Using Resampling Scheme," Journal of Mathematics, Hindawi, vol. 2021, pages 1-12, February.
    7. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    8. Pavia, Jose M., 2015. "Testing Goodness-of-Fit with the Kernel Density Estimator: GoFKernel," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 66(c01).
    9. Sukhdev Singh & Sanku Dey & Devendra Kumar, 2020. "Statistical inference based on generalized Lindley record values," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(9), pages 1543-1561, June.
    10. El-Sherpieny, El-Sayed A. & Almetwally, Ehab M. & Muhammed, Hiba Z., 2020. "Progressive Type-II hybrid censored schemes based on maximum product spacing with application to Power Lomax distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    11. Fernández, Arturo J. & Pérez-González, Carlos J. & Aslam, Muhammad & Jun, Chi-Hyuck, 2011. "Design of progressively censored group sampling plans for Weibull distributions: An optimization problem," European Journal of Operational Research, Elsevier, vol. 211(3), pages 525-532, June.
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    1. 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.

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