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Estimation based on progressive first-failure censoring from exponentiated exponential distribution

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  • Heba S. Mohammed
  • Saieed F. Ateya
  • Essam K. AL-Hussaini

Abstract

In this paper, point and interval estimations for the parameters of the exponentiated exponential (EE) distribution are studied based on progressive first-failure-censored data. The Bayes estimates are computed based on squared error and Linex loss functions and using Markov Chain Monte Carlo (MCMC) algorithm. Also, based on this censoring scheme, approximate confidence intervals for the parameters of EE distribution are developed. Monte Carlo simulation study is carried out to compare the performances of the different methods by computing the estimated risks (ERs), as well as Akaike's information criteria (AIC) and Bayesian information criteria (BIC) of the estimates. Finally, a real data set is introduced and analyzed using EE and Weibull distributions. A comparison is carried out between the mentioned models based on the corresponding Kolmogorov–Smirnov (K–S) test statistic to emphasize that the EE model fits the data with the same efficiency as the other model. Point and interval estimation of all parameters are studied based on this real data set as illustrative example.

Suggested Citation

  • Heba S. Mohammed & Saieed F. Ateya & Essam K. AL-Hussaini, 2017. "Estimation based on progressive first-failure censoring from exponentiated exponential distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(8), pages 1479-1494, June.
    • Handle: RePEc:taf:japsta:v:44:y:2017:i:8:p:1479-1494
    DOI: 10.1080/02664763.2016.1214245
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    References listed on IDEAS

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    1. 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.
    2. Essam AL-Hussaini, 2010. "Inference based on censored samples from exponentiated populations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 487-513, November.
    3. Abdel-Hamid, Alaa H. & AL-Hussaini, Essam K., 2009. "Estimation in step-stress accelerated life tests for the exponentiated exponential distribution with type-I censoring," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1328-1338, February.
    4. 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.
    5. Kundu, Debasis & Gupta, Rameshwar D., 2008. "Generalized exponential distribution: Bayesian estimations," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1873-1883, January.
    6. 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.
    7. 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.
    8. Gupta, Rameshwar D. & Kundu, Debasis, 2003. "Discriminating between Weibull and generalized exponential distributions," Computational Statistics & Data Analysis, Elsevier, vol. 43(2), pages 179-196, June.
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    Cited by:

    1. Abdullah Fathi & Al-Wageh A. Farghal & Ahmed A. Soliman, 2022. "Bayesian and Non-Bayesian Inference for Weibull Inverted Exponential Model under Progressive First-Failure Censoring Data," Mathematics, MDPI, vol. 10(10), pages 1-19, May.
    2. 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.

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