This paper introduces a new calibration estimation technique for the estimation of the population distribution function (DF). We have introduced a new class of calibrated estimators using the non-linear constraints of an auxiliary variable in a simple random sampling design. Their performances have been assessed based on some real and artificially generated data sets under numerical and simulation studies. It has been found that the proposed estimators attain lower absolute relative bias (ARB), lower mean squared error (MSE) and higher percentage relative efficiency (PRE) against the usual unbiased, ratio, product, regression and GREG estimators. The results highlight the effectiveness of the proposed estimators, which may further encourage survey practitioners in their real-life applications.
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