On the Class of Exponential-Type Imputation Estimators of Population Mean with Known Population Mean of Auxiliary Variable

Abstract

This paper considered a new class of exponential-type imputation
scheme and the point estimator of the proposed scheme for estimating
population mean was derived. Members of the derived estimator for
different pairs of constants
1
and K2 ((k1=1, k2=1), (k1=1, k2=-1),
(k1=-1, k2=1), (k1=-1, k2=-1)) were obtained. The properties (bias
and MSE) of the proposed estimator were derived up to second degree
approximation using Taylor’s series procedure. Efficiency conditions
for which the new class of estimators outperformed their counterparts
were also derived by theoretically compared their MSEs. Empirical
study was conducted through simulations using four probability
distributions. The numerical results revealed that the members of the
proposed estimator have less biases, smaller MSEs and larger PREs
compared to other estimators in the study.