Weighted inverted Weibull distribution: Properties and estimation

Abstract

In this article, we provide a comprehensive account of the mathematical properties of the weighted inverted Weibull distribution. Furthermore, we compare different methods of estimation of the unknown parameters of a three-parameter Weighted Inverted Weibull distribution (WIWD) from the frequentist points of view. These methods include the maximum likelihood estimators, moments estimators, least squares estimators, weighted least square estimators, method of maximum product of spacings, method of Cramér-von-Mises, methods of Anderson-Darling and right-tail Anderson-Darling method, respectively. These methods are compared using extensive numerical simulations for both small and large samples. Besides, Bayesian estimation under five different types of loss function (symmetric and asymmetric loss functions) using independent gamma priors for the shape and scale parameters is also discussed. The Bayes estimators and their respective standard deviations are computed and compared by using MCMC technique for both small and large samples. Finally, a real data set has been analyzed for illustrative purposes.

Subject Classification: (2010):

• 62F15
• 62F10
• 62F99

Keywords:

• Bayes estimator
• Hazard rate
• Maximum likelihood estimator
• Moments
• Weighted Inverted Weibull distribution