An improved family of unbiased ratio estimators for a population distribution function

This study discusses a novel family of unbiased ratio estimators using the Hartley-Ross (HR) method. The estimators are designed to estimate the population distribution function (PDF) in the context of simple random sampling with non-response. To assess their performance, expressions for variance are obtained up to the initial (first) approximation order. The efficiency of the proposed estimators is evaluated analytically and numerically compared to existing estimators. In addition, the accuracy of the estimators is assessed using four real-world datasets and a simulation analysis. The proposed estimator demonstrates exceptional performance for the distribution function under simple random sampling, achieving percentage relative efficiencies of 272.052,301.279,214.1214, and 280.9528 across four distinct populations, significantly outperforming existing estimators. For the distribution function under non-response using different weights, the proposed estimator exhibits remarkable efficiency, with percentage relative efficiencies of $w_1$ = 339.7875, $w_2$ = 334.6623, $w_3$ = 337.7393 in Population 1, $w_1$ = 257.0119, $w_2$ = 274.7351, $w_3$ = 316.0341 in Population 2, $w_1$ = 231.8627, $w_2$ = 223.0608, $w_3$ = 219.9059 in Population 3, and $w_1$ = 261.3122, $w_2$ = 242.7319, $w_3$ = 240.0694 in Population 4, validating its robustness and superiority.