Generalized Fiducial Inference for the Chen Distribution

Abstract

The fiducial inference idea was firstly proposed by Fisher [8] as a powerful method in statistical inference. Many authors such as Weeranhandi [24] and Hannig et. al. [12] improved this method from different points of view. Since the Bayesian method has some deficiencies such as assuming a prior distribution when there was little or no information about the parameters, the fiducial inference is used to overcome these adversities. This study deals with the generalized fiducial inference for the shape parameters of the Chen’s two-parameter lifetime distribution with bathtub shape or increasing failure rate [4]. The method based on the inverse of the structural equation which is proposed by Hannig et. al. [12] is used. We propose the generalized fiducial inferences of the parameters with their confidence intervals. Then, these estimations are compared with their maximum likelihood and Bayesian estimations. Simulation results show that the generalized fiducial inference is more applicable than the other methods in terms of the performances of estimators for the shape parameters of the Chen distribution. Finally, a real data example is used to illustrate the theoretical outcomes of these estimation procedures

Keywords

• Bayesian Inference
• Generalized fiducial inference
• Interval estimation
• Chen distribution
• Point Estimation

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