Abstract
This article discusses the estimation of the Generalized Power Weibull parameters using the maximum product spacing (MPS) method, the maximum likelihood (ML) method and Bayesian estimation method under squares error for loss function. The estimation is done under progressive type-II censored samples and a comparative study among the three methods is made using Monte Carlo Simulation. Markov chain Monte Carlo (MCMC) method has been employed to compute the Bayes estimators of the Generalized Power Weibull distribution. The optimal censoring scheme has been suggested using two different optimality criteria (mean squared of error, Bias and relative efficiency). A real data is used to study the performance of the estimation process under this optimal scheme in practice for illustrative purposes. Finally, we discuss a method of obtaining the optimal censoring scheme.
Highlights
Many distributions have been used to make inferences about population based on a set of empirical data from these population
Due to the fact that the relationships between the performance of estimator for generalized power Weibull (GPW) distribution and the censoring scheme are depending on the choice of estimation procedure, we focus our discussion on comparing different types of progressive censoring scheme, type-II censoring scheme and complete censoring scheme based on the maximum product spacing (MPS) method, which is the estimation methods we recommend based on the simulation results
A comparison had been done between the proposed estimators on the basis of Monte Carlo Simulation study
Summary
Many distributions have been used to make inferences about population based on a set of empirical data from these population. Ng et al (2012) introduced estimation of parameters for a three-parameter Weibull distribution based on progressively Type-II right censored samples using the ML method, corrected ML method, weighted ML method, MPS method and least squares estimation method. Singh et al (2016) proposed estimation of generalized inverted exponential distribution (GIED) based on progressive type-II censored samples. Basu et al (2018) discussed the maximum product of spacing estimator for a Progressive hybrid Type-I censoring scheme for inverse Lindley distribution. Almetwaly and Almongy (2018) discussed the complete censoring as a special case of the progressive type-II censoring scheme when estimating the GPW distribution parameters. The aim of this paper is to estimate the parameters of the GPW model under Progressive Type-II Censoring Schemes. We show the results and the conclusion of the current study
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