Estimation of the shape parameter of a Pareto distribution

ABSTRACT

We consider the problem of estimating the shape parameter of a Pareto distribution with unknown scale under an arbitrary strictly bowl-shaped loss function. Classes of estimators improving upon minimum risk equivariant estimator are derived by adopting Stein, Brown, and Kubokawa techniques. The classes of estimators are shown to include some known procedures such as Stein-type and Brewster and Zidek-type estimators from literature. We also provide risk plots of proposed estimators for illustration purpose.

KEYWORDS:

• Improved estimators
• integral expression of risk difference
• scale invariance.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F10
• 62C15

Acknowledgements

The authors are thankful to a referee and the Editor for their helpful comments which significantly improved the presentation of this paper. The research work of Yogesh Mani Tripathi is partially supported by a grant SR/S4/MS: 785/12 from SERB, Department of Science and Technology, India.