Improved estimator of population total in PPS sampling

In this paper, we have considered an estimation of the population total Y of the study variable y, making use of information on an auxiliary variable x. A class of estimators for the population total Y using transformation on both the variables study as well as auxiliary has been suggested based on the probability proportional to size with replacement (PPSWR). In addition to many the usual PPS estimator, Reddy and Rao's (1977) estimator and Srivenkataramana and Tracy's (1979, 1984, 1986) estimators are shown to be members of the proposed class of estimators. The variance of the proposed class of estimators has been obtained. In particular, the properties of 75 estimators based on different known population parameters of the study as well as auxiliary variables have been derived from the proposed class of estimators. In support of the present study, numerical illustrations are given.