The efficiency of an alternative to ratio estimator under a super population model

Abstract

Srivenkataramana and Tracy (1986) have suggested an alternative to ratio estimator. Its efficiency relative to usual unbiased estimator, ratio estimator and product estimator based on simple random sampling without replacement (SRSWOR) is studied under a super population model with uncorrelated error and a gamma distributed auxiliary character. It has been shown that the estimator forwarded by Srivenkataramana and Tracy (1986) is inferior to usual ratio estimator except when variance of study variate is constant (i.e. g=0). However, their estimator is better than the usual unbiased estimator and product estimator for a wide range of a constant involved in the estimator. Results have been supported with some numerical examples.