The problem of generalized estimation methods of population distribution functions with auxiliary information: The international trade and radiation measurements

The precise computation of population distribution function is essential in numerous scientific and environmental research especially where there is high variability of data or uncertainty of measurements. This paper suggests new generalized class of estimators for the population distribution function that magnificently utilizes the auxiliary information to enhance accuracy and efficiency. As compared to other traditional estimators which use only primary survey information, the proposed work uses auxiliary information that are correlated to the study variable in order to minimize bias and mean squared error (MSE). The generalized classes of estimators are constructed in the same framework which includes multiple popular distribution function estimators as special cases. Analytic forms of the bias and MSE have been obtained to the first order of approximation and efficiency comparisons have been made in order to bring out the performance improvements that arise under different sampling conditions. To illustrate useful application, the approach is used on radiation data, a field where it is crucial to have a reliable estimation of population distribution function to assess the risks of health and environment monitoring. As the numerical findings indicate, the suggested estimators are better than traditional counterparts in precision and strength especially when the auxiliary information is significantly correlated with the variable of interest. In general, this work offers an effective and adaptable model of distribution functions estimation with the help of auxiliary information. The proposed class of estimators provides effective benefits as compared to adopted existing estimators.