A comparison of different methods of estimation for the flexible Weibull distribution

Abstract

This article presents different parameter estimation methods for flexible Weibull distribution introduced by Bebbington et al. (Reliability Engineering and System Safety 92:719-726, 2007), which is a modified version of the Weibull distribution and is suitable to model different shapes of the hazard rate. We consider both frequentist and Bayesian estimation methods and present a comprehensive comparison of them. For frequentist estimation, we consider the maximum likelihood estimators, least squares estimators, weighted least squares estimators, percentile estimators, the maximum product spacing estimators, the minimum spacing absolute distance estimators, the minimum spacing absolute log-distance estimators, Cramér von Mises estimators, Anderson Darling estimators, and right tailed Anderson Darling estimators, and compare them using a comprehensive simulation study. We also consider Bayesian estimation by assuming gamma priors for both shape and scale parameters. We use a Markov Chain Monte Carlo algorithm to compute the posterior summaries. A real data example is also a part of this work.

Keywords

• Weibull distribution; maximum likelihood estimators; least square estimators; weighted least square estimators; percentile estimators; maximum product spacing estimators; minimum spacing absolute distance estimators; minimum spacing absolute log-distance estimators; Cramer von Mises estimators; Anderson Darling estimators; right tailed Anderson Darling estimators; Bayesian estimation.

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