A new logarithmic type estimator for estimation of population distribution function: Its case studies in cultural communication and radiation sciences

This paper introduces improved logarithmic type estimator to estimate the finite population distribution function (DF) using two auxiliary variables. The proposed estimator aims to make better use of the auxiliary information than the existing estimators, for better estimation precision. The use of a logarithmic functional form is used to make the estimator efficient when the auxiliary variables are correlated with the study variable. First-order approximation is used to derive the statistical properties such as bias and the mean squared error. Theoretical efficiency conditions are obtained that characterize conditions under which the proposed estimator is more efficient than some of the other estimators of the population DF. Empirical studies are carried out with actual data on cultural communication and radiation sciences to evaluate the practical performance. The numerical results show that the proposed estimator has the lowest MSE and the highest PREs than the other competing estimators in study. The results indicate that the simultaneous application of two related auxiliary variables can yield significant gains in the accuracy of the estimation of the population DF. Hence the proposed approach offers a generally applicable and efficient framework for finite population inference and might be especially suitable in applications for which reliable auxiliary information is easily available, such as cultural, communication, environmental, medical, and radiation-related studies.