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.

In this study, we proposed novel estimators for finite population variance based on the raw moments of the study and auxiliary variables. Specifically, we developed both biased and unbiased estimators of variance using the raw moments of the study variable alone, as well as biased and unbiased difference-type estimators that incorporate the raw moments of a single auxiliary variable. These estimators were evaluated under two-stage cluster sampling (2SCS) and three-stage cluster sampling (3SCS) schemes. Their performance, with and without auxiliary information, was assessed using mean squared error (MSE), absolute bias (AB), and relative efficiency (RE) criteria. Results from two real populations showed that AB decreases and RE improves with increasing sample size. Notably, under 3SCS, the unbiased difference estimator, ${\hat{S}}_{Y,DU}^2$, achieved the highest efficiency ( $R{E}_3=527.69$), closely followed by the biased difference estimator, ${\hat{S}}_{Y,DB}^2$ ( $R{E}_4=527.26$). Both estimators substantially outperformed conventional variance estimators without auxiliary information (baseline $RE$ = 100). These findings demonstrate that incorporating auxiliary variables significantly enhances estimation accuracy, offering a practical and robust approach for variance estimation in complex survey designs.