On inverse sampling with unequal probabilities

Abstract

Sampford (1962) has considered the following sampling scheme to select a sample with n distinct population units. Sampling with unequal probabilities with replacement is carried out until (n+1) different population units are selected, the last unit is not recorded in the sample to insure some simplicity in the estimation procedure. The method is called inverse sampling with unequal probabilities. In this paper it is shown that this method of sampling is equivalent to sampling with unequal probabifities without replacement in some sense. The estimator of the population total given by Sampford is compared with other existing estimators. It is shown that there exist estimators which are uniformly better than the estimator given by Sampford. Finally, it is demonstrated that Des Raj's estimator (1956) has certain definite advantages over Sampford's estimator suggesting that sampling with unequal probabilities (without replacement) with Des Raj's estimator probably gives a better estimation procedure than inverse sampling with unequal probabilities.