A Novel Logarithmic-Exponential Cum Ratio-Type Estimator Under Simple Random Sampling

Abstract

In sample surveys, the use of auxiliary variables to estimate the population mean has become crucial for improving the efficiency of the estimators, including traditional ratio, product and regression estimators. This paper introduces a new logarithmic-exponential cum ratio-type estimator for the elevated estimation of population mean under simple random sampling. We have obtained the bias and mean squared error (MSE) of the proposed estimator up to the first order of approximation and identified the situations in which it performs more efficiently than existing estimators. To verify the theoretical results, we have conducted numerical study based on eight real data sets belonging from the clinical, agricultural and business fields. Their performances have also been evaluated through  simulation study that utilized two artificially generated datasets. A sensitivity analysis based on the sample estimates has been investigated to reassert the behaviours of proposed estimators.

Keywords: Study variable; Auxiliary variable; Population mean; Mean squared error; Percent Relative Efficiency.

2010 Mathematics Subject Classification. 62D05