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.
Highlights
In industrial life testing and medical survival analysis, very often the object of interest is lost or withdrawn before failure or the object lifetime is only known within anB Rashad M
The purpose of this paper is to develop different methods to estimate and construct confidence intervals for the parameters as well as reliability function, hazard function and coefficient of variation of the Weibull–Gamma distributed under a progressively type-II censored samples
Because of that we have used Markov chain Monte Carlo (MCMC) technique and it is observed that the Bayes estimate with respect to informative prior works quite well in this case
Summary
In industrial life testing and medical survival analysis, very often the object of interest is lost or withdrawn before failure or the object lifetime is only known within an. Aggarwala and Balakrishnan (1998) developed an algorithm to simulate general, progressively type-II censored samples from the uniform or any other continuous distribution. Gibbs sampler requires only the specification of the conditional posterior distribution for each parameter In situations where those distributions are simple to sample from, the approach is implemented. Statistical inference for unknown parameters of WGD has not yet been studied under progressive type-II censoring. Maximum likelihood and Bayesian inference of unknown parameters as well as reliability function, hazard function and coefficient of variation will be studied under progressive type-II censoring. 2, discusses the maximum likelihood estimators (MLEs) of the unknown parameters, reliability function, hazard function and coefficient of variation. 4, we introduce two parametric bootstrap procedures to construct the confidence intervals for the unknown parameters, reliability function, hazard function and coefficient of variation.
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