Reliability Estimation and Parameter Estimation for Inverse Weibull Distribution Under Different Loss Functions
Keywords:Lindley’s approximation, Loss function, MCMC method, Parameter estimation, Reliability estimation.
In this paper, the classical and Bayesian estimators of the unknown parameters and reliability
function of the inverse Weibull distribution are considered. The maximum likelihood estimators
(MLEs) and modified maximum likelihood estimators (MMLEs) are used in the classical
parameter estimation. Bayesian estimators of the parameters are obtained by using symmetric and asymmetric loss functions under non-prior and prior distributions. Bayesian computation are derived by using Lindley approximation and Markov chain Monte Carlo (MCMC) methods. The asymptotic confidence intervals are constructed based on the maximum likelihood estimators. The Bayes credible intervals of the parameters are obtained by using MCMC method. Furthermore, the performances of these estimation methods are compared with respect to their biases and mean square errors through a simulation study. It is seen that the Bayes estimators perform better than the classical estimators. Finally, two real life examples are given for illustrative purposes.
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