Development and Evaluation of EDM: An Exponential Decay Model for Probability Estimation in Random Sampling with Replacement

The article presents a novel probability estimation model designed to predict the likelihood of selecting k units from a group of size n within a population of N units in the context of random sampling with replacement. The traditional method for computing these probabilities requires significantly higher computational resources. In this scenario, the proposed exponential decay model offers a more efficient alternative, reducing the computational burden. The proposed model leverages the exponential decay function, yielding an equation utilising Euler’s number to predict probabilities. The model takes k:N and n:N ratios as inputs, thereby making it adaptable to diverse sampling schemes. The methodology for developing the proposed Exponential Decay Model (EDM) applied a systematic approach involving a multi-tiered equation. To assess the model’s effectiveness, we compare its performance against five other statistical and Machine Learning-based models (including Decision Tree, Random Forest, Linear Regression, Nearest neighbour and Support Vector regression) employing the Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Coefficient of Determination ( \(r^2\) $r^2$ ) metrics. The results demonstrate that the proposed EDM outperforms its counterparts, yielding outstanding scores with the RMSE and MAE < 0.01 and an \(r^2\) $r^2$ > 0.9. The study contributes an innovative approach for probability estimation in sampling with replacement, presenting a robust model that outperforms alternative models, thus offering valuable insights and applications in the field of sampling and statistical analysis.