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Estimation of the parameters of life for Gompertz distribution using progressive first-failure censored data

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  • Soliman, Ahmed A.
  • Abd-Ellah, Ahmed H.
  • Abou-Elheggag, Naser A.
  • Abd-Elmougod, Gamal A.

Abstract

Bayes and frequentist estimators are obtained for the two-parameter Gompertz distribution (GD), as well as the reliability and hazard rate functions, using progressive first-failure censoring plan. We have examined Bayes estimates under symmetric and asymmetric loss functions. We show that the Bayes estimates relative to asymmetric loss function includes the maximum likelihood estimate (MLE) and other Bayes estimates as special cases. This is done using the conjugate prior for the scale parameter and discrete prior for the shape parameter. It has been seen that the Bayes estimators are obtained in closed form. Also, based on this new censoring scheme, exact and approximate confidence intervals as well as exact confidence region for the parameters of GD are developed. A practical example using simulated data set was used for illustration. Finally, to assess the performance of the proposed estimators, numerical results using Monte Carlo simulation study were reported.

Suggested Citation

  • Soliman, Ahmed A. & Abd-Ellah, Ahmed H. & Abou-Elheggag, Naser A. & Abd-Elmougod, Gamal A., 2012. "Estimation of the parameters of life for Gompertz distribution using progressive first-failure censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2471-2485.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:8:p:2471-2485
    DOI: 10.1016/j.csda.2012.01.025
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    References listed on IDEAS

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    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. Ng, H. K. T. & Chan, P. S. & Balakrishnan, N., 2002. "Estimation of parameters from progressively censored data using EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 371-386, June.
    3. 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.
    4. 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.
    5. Soliman, Ahmed A. & Abd Ellah, A.H. & Sultan, K.S., 2006. "Comparison of estimates using record statistics from Weibull model: Bayesian and non-Bayesian approaches," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 2065-2077, December.
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    Cited by:

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    3. Mohammed S. Kotb & Huda M. Alomari, 2024. "Estimating the entropy of a Rayleigh model under progressive first-failure censoring," Statistical Papers, Springer, vol. 65(5), pages 3135-3154, July.
    4. Tzong-Ru Tsai & Hua Xin & Chiun-How Kao, 2021. "Bayesian Estimation Based on Sequential Order Statistics for Heterogeneous Baseline Gompertz Distributions," Mathematics, MDPI, vol. 9(2), pages 1-21, January.
    5. Muqrin A. Almuqrin & Mukhtar M. Salah & Essam A. Ahmed, 2022. "Statistical Inference for Competing Risks Model with Adaptive Progressively Type-II Censored Gompertz Life Data Using Industrial and Medical Applications," Mathematics, MDPI, vol. 10(22), pages 1-38, November.
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