Optimal estimation for the Pareto distribution

Abstract

This paper proposes an optimal estimation method for the shape parameter, probability density function and upper tail probability of the Pareto distribution. The new method is based on a weighted empirical distribution function. The exact efficiency functions of the estimators relative to the existing estimators are derived. The paper gives L ₁-optimal and L ₂-optimal weights for the new weighted estimator. Monte Carlo simulation results confirm the theoretical conclusions. Both theoretical and simulation results show that the new estimation method is more efficient relative to several existing methods in many situations.

Keywords:

• efficiency
• order statistics
• weighted empirical distribution function
• density estimation
• Pareto upper tail

AMS 1991 Subject Classifications :

• Primary: 62G30
• Secondary: 62G05

Acknowledgements

Research of the author is supported by an NSERC Canada grant.