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

• Published in: Computational statistics & data analysis Vol. 56; no. 8; pp. 2471 - 2485
• Main Authors: Soliman, Ahmed A., Abd-Ellah, Ahmed H., Abou-Elheggag, Naser A., Abd-Elmougod, Gamal A.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.08.2012; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Bayesian analysis; Bayesian estimator; Computer simulation; Confidence intervals; Confidence regions; Estimates; Estimators; Gompertz distribution; Gompertz distribution Progressive first-failure censoring scheme Symmetric and asymmetric loss functions Maximum likelihood estimator Bayesian estimator Confidence intervals Confidence regions; Mathematical analysis; Mathematical models; Maximum likelihood estimator; Monte Carlo methods; Progressive first-failure censoring scheme; Symmetric and asymmetric loss functions; Maximum likelihood estimator; Confidence intervals; Confidence regions; Gompertz distribution; Progressive first-failure censoring scheme; Bayesian estimator; Symmetric and asymmetric loss functions
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2012.01.025

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.