Original title: Development of Efficient Transformed Ratio-Type Estimators for Finite Population Mean with Engineering Applications
Abdulrahman Obaid Alshammari · September 2026
Scientists often need to estimate the average value of a group without checking every single member. If they already have extra, related data, they can make their estimate much more accurate. To do this, researchers designed two new groups of estimation formulas for random sampling without replacement. These formulas mix ratio and exponential mathematical patterns with tuned linear correction terms. They also apply seven different transformations to the extra data. A single factor connects these transformations to show how each one changes data variability. Tests showed that the new formulas perform well across many tests, especially when the two types of data share a moderate or high correlation. However, no single transformation wins in every case. Real accuracy depends on the correlation strength, the sample size, and picking the right transformation factor. In some settings, a standard regression estimator is still hard to beat.
You are trying to guess the total weight of all luggage on a flight by weighing a few suitcases. A simple average of those few suitcases gives a rough guess, but if you also know the total number of suitcases, you can multiply the average by that count. Now imagine the number of suitcases is uncertain itself — it shifts depending on which suitcases you weighed first. In this paper that uncertainty about the correction factor is modeled explicitly, and the estimator is adjusted so the guess stays accurate even when the relationship between weight and count is different for different flights.
Engineers and surveyors often need to estimate the average of something — like material strength or crop yield — from a sample. This paper gives them a set of mathematical tools to shrink their error by pulling in a second, easier-to-measure variable, like temperature or soil moisture. Better estimates with the same data mean cheaper surveys, smaller safety margins, and more confident decisions.
The theoretical derivations rely on first-order Taylor approximation, so bias expressions are approximate for small samples. The engineering application results are based on population summaries from the source study, not full original data, making them first-order comparisons. The regression estimator remains hard to beat in some settings, and the optimal constant requires plug-in estimation when it contains the unknown population mean.
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Development of Efficient Transformed Ratio-Type Estimators for Finite Population Mean with Engineering Applications — Abdulrahman Obaid Alshammari — Mathematics — doi:10.3390/math14183404
Abstract licence: CC BY
Explanation generated by Synthesis from the abstract — it is not the original paper.