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

• DOI: 10.3934/math.2025051
• Publication Date: 2025-01-17T10:32:41Z
• Authors: Sohail Ahmad; Moiz Qureshi; Hasnain Iftikhar; Paulo Canas Rodri...; Mohd Ziaur Rehman
• Keywords: U-statistic

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