Performance Comparison of Three Ratio Estimators of the Population Ratio in Simple Random Sampling Without Replacement

This study aims to compare the efficacy of three ratio estimators for estimating the population ratio in simple random sampling without replacement (SRSWOR). The estimators under consideration are a customary ratio estimator (~R1), a ratio estimator based on a transformed mean estimator (~R2) introduced by Onyeka et al. [1], and a regression-type estimator (~R3) proposed by Onyeka et al. [2]. We assess the performance of these estimators across three distributions (bivariate normal, bivariate Poisson log-normal, and bivariate Cauchy) while varying both correlation coefficients and sample sizes, utilizing Mean Square Error (MSE) and Percent Relative Efficiency (PRE) as evaluation criteria. The results indicate that for a bivariate normal distribution, the ~R1 and ~R2 estimators consistently outperformed the ~R3 estimator across all sample sizes and correlation coefficients. The ~R2 estimator demonstrated superiority with very small sample sizes, while ~R1 exhibited better performance in small sample sizes. The ~R2 estimator remained reliable for moderately sized samples, demonstrating consistent efficiency. In large samples, ~R2 maintained its performance advantage, except in weak correlation coefficients, where ~R1 proved superior. For a bivariate Poisson lognormal distribution, both ~R2 and ~R3 performed significantly better than ~R1 for very small sample sizes, irrespective of correlation direction and strength. For moderately sized samples, ~R2 and ~R3 consistently excelled, with ~R2 leading in cases with positive correlation coefficients. For large sample sizes with negative correlation coefficients, both ~R2 and ~R3 were comparable effective and significantly better than ~R1. Conversely, with positive correlation coefficients, the ~R1 estimator significantly outperformed both ~R2 and ~R3. In a bivariate Cauchy distribution, the ~R1 estimator demonstrated notable and consistent superiority over the ~R2 and ~R3 estimators across all sample sizes and correlation coefficients.