Bayes Shrinkage Estimation of the Parameter of Rayleigh Distribution for Progressive Type-II Censored Data

Sanku Dey,Sudhansu S Maiti,Tanujit Dey

doi:10.17713/ajs.v44i4.71

Abstract

This paper derives Bayes shrinkage estimator of Rayleigh parameter and its associated risk based on conjugate prior under the assumption of general entropy loss function for progressive type-II censored data. Risk function of maximum likelihood estimate, Bayes estimate and Bayes shrinkage estimate have also been derived and compared. A procedure has been suggested to include a guess value in case of the Bayes shrinkage estimation. Risk function of empirical Bayes estimate and empirical Bayes shrinkage estimate have also been derived and compared. In conclusion, an illustrative example is presented to assess how the Rayleigh distribution fits a real data set.

Highlights

Rayleigh distribution first introduced in the literature by Lord Rayleigh (1980) has been widely used in reliability theory and survival analysis because of it’s flexibility and simplicity
Chen, and Chen (2006) obtained Bayes estimators and highest posterior density credible intervals for parameter and reliability function of the Rayleigh distribution, as well as the Bayes predictive estimator and prediction interval for future observations based on progressively Type-II censored samples
The key goal of our article is to obtain Bayes estimator and Bayes shrinkage estimator for the parameter of Rayleigh distribution with conjugate prior distribution based on progressively Type-II censored samples

Summary

Introduction

Rayleigh distribution first introduced in the literature by Lord Rayleigh (1980) has been widely used in reliability theory and survival analysis because of it’s flexibility and simplicity. Howlader and Hossain (1995) obtained Bayes estimators for the scale parameter and the reliability function in the case of Type-II censored sampling. Wu, Chen, and Chen (2006) obtained Bayes estimators and highest posterior density credible intervals for parameter and reliability function of the Rayleigh distribution, as well as the Bayes predictive estimator and prediction interval for future observations based on progressively Type-II censored samples. Dey (2009) studied the Bayes estimators for the parameter and reliability function of Rayleigh distribution based on complete as well as Type-II censored samples, compared relative risk functions. Singh, Singh, Singh, and Upadhyay (2008) studied the Bayes estimators of the failure rate and reliability function for a one-parameter exponential distribution by utilizing a point guess estimate of the parameter. One censoring scheme known as progressive Type-II censoring scheme overcomes this shortcoming and this has led to its popularity in recent years

Review of progressive Type-II sampling

Prior and loss function

Estimation

Simulation study

Data analysis

Conclusion