Advances and Applications in Statistics
Volume 45, Issue 1, Pages 1 - 27
(April 2015) http://dx.doi.org/10.17654/ADASApr2015_001_027 |
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ESTIMATION OF THE PARAMETERS OF LIFE FOR DISTRIBUTIONS HAVING POWER HAZARD FUNCTION BASED ON PROGRESSIVELY TYPE-II CENSORED DATA
Rashad M. El-Sagheer
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Abstract: In this paper, we investigate the problem of point and interval estimations of the parameters, reliability and hazard functions for distributions having power hazard function when sample is available from progressive type-II censoring scheme. The maximum likelihood, Bayes, and parametric bootstrap methods are used for estimating the unknown parameters as well as some lifetime parameters (reliability and hazard functions). Based on the asymptotic normality of the maximum likelihood estimators, the approximate confidence intervals (ACIs) are obtained. Moreover, in order to construct the asymptotic confidence intervals of the reliability and hazard functions, we need to find the variance of reliability and hazard functions, which are approximated by delta and parametric bootstrap methods. The Markov chain Monte Carlo (MCMC) technique is used to compute the Bayes estimates of the parameters. Gibbs within the Metropolis-Hasting algorithm has been applied to generate MCMC samples from the posterior density function. Based on the generated samples, the Bayes estimates and highest posterior density credible intervals of the unknown parameters as well as reliability and hazard functions have been computed. The results of Bayes method are obtained under both the balanced squared error (BSE) loss and balanced linear-exponential (BLINEX) loss. Finally, a numerical example using the real data set is provided to illustrate the proposed estimation methods developed here. |
Keywords and phrases: distributions having power hazard function, progressive type-II censoring, maximum likelihood estimator, delta and parametric bootstrap methods, Bayesian estimator, MCMC technique, balanced loss function. |
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