Shrinkage estimator for scale parameter of gamma distribution

Abstract

In this article, we propose a shrinkage estimator for the scale parameter of the Gamma distribution when the prior information is available and compare it with minimum mean square error (MMSE) of its usual estimator in the sense of efficiency. The proposed shrinkage estimator has smaller Mean Square Error (MSE) than MMSE estimator when the prior estimate is good. The properties of shrinkage estimator have been studied in terms of bias and mean square error. Numerical illustrations are carried out to throw light on the performance of the proposed method of estimation other conventional estimators.

Keywords:

• Gamma distribution
• Minimum mean square error
• Minimum variance unbiased estimator
• Scale Parameter
• Shrinkage estimator

MATHEMATICS SUBJECT CLASSIFICATION:

• 62D05
• 60E05
• 62E99

Acknowledgment

Authors are deeply indebted to the editor-in-chief Professor Narayanaswamy Balakrishnan and learned referees for their constructive suggestions leading to improving the quality and contents of the manuscript.