Shrinkage Bayesian Estimator for the Scale Parameter of the Two Parameter Exponential Distribution under Progressive Censored Type-II Data and Generalized Entropy Loss Function

Subject Areas : Statistics

Mehdi Bazyar Dizabadi ¹ , Einolah Deiri ² , Ezzatallah baloui Jamkhaneh ³

1 - Department of Statistics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
2 - Department of Statistics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
3 - Department of Statistics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran

Received: 2019-10-03 Accepted : 2021-04-27 Published : 2021-05-22

Keywords: توزیع نمایی دوپارامتری, تابع زیان آنتروپی تعمیم یافته, طرح سانسور نوع دوم فزاینده, برآوردگر بیزی انقباضی,

Abstract :

Our main objective in this paper is to analyze Bayesian Shrinkage Estimators of the parameter of two-parameter Exponential Distribution Scale under General Entropy Loss Function based on the prior conjugate distribution and Progressive Type-II Censored Data in the presence of the location parameter. To this end, in the present paper, firstly, we present Shrinkage Estimator of scale parameter based on the Bayesian estimator that obtained under General Entropy Loss Function, and prior conjugate distribution, and then investigate the efficiency of the proposed estimator with other estimators, such as maximum likelihood estimator, Bayes estimator, empirical Bayesian estimator, and empirical Bayesian Shrinkage Estimator. The method used in this paper to compute empirical Bayesian estimator, and empirical Bayesian Shrinkage Estimator is guessing. Using simulated data based on Monte Carlos’ method, under six censorship schemes and with two prior distributions of Jeffrey and Hartigan, the effectiveness of estimators is compared. Finally, using actual data, the efficiency of the proposed estimators will be examined.

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