Unbiased estimation of P (X>Y) for two-parameter exponential populations using order statistics

Abstract

The problem considered is that of unbiased estimation of P [X>Y] (=θ) for two independent random variables X and Y each following a two-parameter exponential distribution. We give necessary and sufficient conditions for the existence of an unbiased estimator of θ based on arbitrary sets of order statistics obtained from independent random samples from the two populations and suggest unbiased estimators in some situations where unbiased estimators exist.

Keywords:

• exponential population
• order statistics
• unbiased estimation

AMS (2000) Classification :

• 62D05
• 62F10

Acknowledgements

The author is thankful to the referee for his helpful comments and suggestions on an earlier draft of the paper.