Unbiased Estimation of the Distribution Function of an Exponential Population Using Order Statistics with Application in Ranked Set Sampling

Abstract

In this paper we consider the problem of unbiased estimation of the distribution function of an exponential population using order statistics based on a random sample. We present a (unique) unbiased estimator based on a single, say ith, order statistic and study some properties of the estimator for i = 2. We also indicate how this estimator can be utilized to obtain unbiased estimators when a few selected order statistics are available as well as when the sample is selected following an alternative sampling procedure known as ranked set sampling. It is further proved that for a ranked set sample of size two, the proposed estimator is uniformly better than the conventional nonparametric unbiased estimator, further, for a general sample size, a modified ranked set sampling procedure provides an unbiased estimator uniformly better than the conventional nonparametric unbiased estimator based on the usual ranked set sampling procedure.

Keywords:

• Distribution function
• Exponential population
• Order statistics
• Ranked set sampling
• Simple random sampling
• Unbiased estimator

AMS (2000) Classification:

• 62D05
• 62F10

Acknowledgment

Research of Sujay Mukhuti is supported by Council of Scientific and Industrial Research, India (Sanction no. 9/28(566)/2002/EMR-I).