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Estimation of parameters of Weibull–Gamma distribution based on progressively censored data

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  • Rashad M. EL-Sagheer

    (A1-Azhar University)

Abstract

In this paper, the estimation of parameters of a three-parameter Weibull–Gamma distribution based on progressively type-II right censored sample is studied. The maximum likelihood, Bayes, and parametric bootstrap methods are used for estimating the unknown parameters as well as some lifetime parameters reliability function, hazard function and coefficient of variation. Approximate confidence intervals for the unknown parameters as well as reliability function, hazard function and coefficient of variation are constructed based on the s-normal approximation to the asymptotic distribution of maximum likelihood estimators (MLEs), and log-transformed MLEs. In addition, two bootstrap CIs are also proposed. Bayes estimates of the unknown parameters and the corresponding credible intervals are obtained by using the Gibbs within Metropolis–Hasting samplers procedure. Furthermore, the results of Bayes method are obtained under both the balanced squared error loss and balanced linear-exponential loss. Analysis of a simulated data set has also been presented for illustrative purposes. Finally, a Monte Carlo simulation study is carried out to investigate the precision of the Bayes estimates with MLEs and two bootstrap estimates, also to compare the performance of different corresponding CIs considered.

Suggested Citation

  • Rashad M. EL-Sagheer, 2018. "Estimation of parameters of Weibull–Gamma distribution based on progressively censored data," Statistical Papers, Springer, vol. 59(2), pages 725-757, June.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:2:d:10.1007_s00362-016-0787-2
    DOI: 10.1007/s00362-016-0787-2
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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. Basak, Prasanta & Basak, Indrani & Balakrishnan, N., 2009. "Estimation for the three-parameter lognormal distribution based on progressively censored data," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3580-3592, August.
    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.
    5. Mohammad Jafari Jozani & Éric Marchand & Ahmad Parsian, 2012. "Bayesian and Robust Bayesian analysis under a general class of balanced loss functions," Statistical Papers, Springer, vol. 53(1), pages 51-60, February.
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    Cited by:

    1. Ruhul Ali Khan & Murari Mitra, 2021. "Estimation issues in the Exponential–Logarithmic model under hybrid censoring," Statistical Papers, Springer, vol. 62(1), pages 419-450, February.
    2. Bo-Hong Wu & Hirofumi Michimae & Takeshi Emura, 2020. "Meta-analysis of individual patient data with semi-competing risks under the Weibull joint frailty–copula model," Computational Statistics, Springer, vol. 35(4), pages 1525-1552, December.
    3. Leijia Ding & Wenhao Gui, 2023. "Statistical Inference of Two Gamma Distributions under the Joint Type-II Censoring Scheme," Mathematics, MDPI, vol. 11(9), pages 1-23, April.
    4. Amel Abd-El-Monem & Mohamed S. Eliwa & Mahmoud El-Morshedy & Afrah Al-Bossly & Rashad M. EL-Sagheer, 2023. "Statistical Analysis and Theoretical Framework for a Partially Accelerated Life Test Model with Progressive First Failure Censoring Utilizing a Power Hazard Distribution," Mathematics, MDPI, vol. 11(20), pages 1-21, October.
    5. Shu-Fei Wu & Meng-Zong Song, 2023. "Experimental Design for Progressive Type I Interval Censoring on the Lifetime Performance Index of Chen Lifetime Distribution," Mathematics, MDPI, vol. 11(6), pages 1-16, March.

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