Maximum Product Spacings Estimator for Fuzzy Data Using Inverse Lindley Distribution

Abstract

The article addresses the problem of parameter estimation of the inverse Lindley distribution when the observations are fuzzy. The estimation of the unknown model parameter was performed using both classical and Bayesian methods. In the classical approach, the estimation of the population parameter is performed using the maximum likelihood (ML) method and the maximum product of distances (MPS) method. In the Bayesian setup, the estimation is obtained using the squared error loss function (SELF) with the Markov Chain Monte Carlo (MCMC) technique. Asymptotic confidence intervals and highest posterior density (HPD) credible intervals for the unknown parameter are also obtained. The performances of the estimators are compared based on their MSEs. Finally, a real data set is analyzed for numerical illustration of the above estimation methods.