Unbiased Estimation of the Distribution Function of a Two-Parameter Exponential Population Using Order Statistics

Abstract

In this article, we consider the problem of unbiased estimation of the distribution function of a two-parameter exponential population using order statistics based on a random sample from the population. We give necessary and sufficient conditions for the existence of an unbiased estimator based on an arbitrary set of order statistics and suggest unbiased estimators in some situations where unbiased estimators exist. A few properties of the suggested estimators for some special cases have also been discussed.

Keywords:

• Distribution function
• Exponential population
• Orders statistics
• Unbiased estimation

Mathematics Subject Classification:

• 62D05, 62F10

Acknowledgment

We are thankful to the referees for their useful comments and suggestions on an earlier draft of the article.