Investigating the role of dual use of an auxiliary variable: A difference-cumexponential estimator

Abstract

The estimation of finite population mean is always of interest for different sampling techniques and it is the basic measure to find from sample to estimate one the most applicable central tendency. In literature, under simple random sampling without replacement people used auxiliary variable, its rank or empirical distribution function in different estimation approaches such as regression, ratio, exponential or combination of these to improve the efficiency of the estimator. In literature, either rank or empirical distribution function have been used while constructing the estimator because both cannot be used due to the fact that empirical distribution function of a variable is based on its rank, therefore, both are perfectly correlated. In this paper, our argument is that the dual use is not effective rather an additional independent auxiliary variable may be effective for efficiency improvement. To investigate this, we proposed difference-cum-exponential estimator using two auxiliary variables and also the dual use of one of the auxiliary variable in the form of its empirical distribution function. We also deduced some special cases of the proposed estimator. These special cases will help us to investigate the argument. The mean square errors of the proposed estimator and its special cases are derived. The proposed estimator, its special cases and potential existing estimators are compared using empirical study based on real life population for numerical investigation of the argument. The simulation study is also conducted for symmetric and skewed populations to asses the sampling stability of the competitive estimators using empirical mean square error and also it will help to further investigate the argument.

Journal of Statistical Research 2025, Vol. 59, No. 1, pp. 81-97