A Superior Optimized Generalized Class of Estimators for Inference of Population Distribution Function Estimation Using Auxiliary Information

This paper presents an efficient improved generalized class of estimators for the precise estimation of the population distribution function using auxiliary information. Estimation of the population distribution function is a crucial aspect of statistical inference, particularly in survey sampling and applied research, where data of the entire population is often inaccessible. Conventional estimators, although popular, may be inefficient if they do not optimally exploit the information on the auxiliary variables associated with the variable under investigation. To overcome this problem, a new class of estimators is proposed by incorporating the known parameters of the auxiliary variables in a functional form. The bias and mean squared error (MSE) of the suggested and existing estimators are obtained under regularity conditions for large samples. Theoretically, the proposed estimators are shown to have lower MSE than the traditional estimators. The results indicate that using additional information significantly improves estimation accuracy. Thus, the proposed class is an important addition to the literature on survey sampling and estimation of distribution functions. This research contributes useful techniques for researchers and offers guidance to enhance estimation accuracy in empirical studies.