Statistical Inference on the Inverse Weibull Model Parameters Based on Dual Generalized Fuzzy Order Statistics

Abstract

Abstract In statistical inference, the parameter estimations for lifetime distribution usually deal with precise information. However, in real-world situations, experimental performance results cannot always be recorded or measured precisely, and each observable event may only be identified with a fuzzy subset of the sample space. The mean objective of this work is to apply Bayes estimation for the inverse Weibull distribution parameters, based on dual generalized fuzzy order statistics when the available observations are described by means of fuzzy information. The Bayesian estimates are compared to the maximum likelihood estimates (MLEs) and the expectation maximization (EM) estimates, via Monte Carlo simulations, in terms of the mean square errors and mean percentage errors. The results are quite favorable to Bayes’ method, which provides better estimates and outperforms the maximum likelihood and the EM estimates for different sample sizes and several values for the true parameters. Finally, a numerical example is given to demonstrate the efficiency of the proposed method.