Details of Research Outputs

In statistical simulations, using representative samples is crucial for obtaining accurate, unbiased, and generalizable results. Random samples often fail to represent the original distribution, leading to substantial deviations from the original distribution and mismatches in the predefined mean and variance. (Formula presented.) We propose a method for generating representative samples from a continuous distribution that minimizes the mean square error (MSE) between the sample and the original distribution while ensuring the first two sample moments match preset values. (Formula presented.) These samples are called moment-constrained mean square error representative samples (MCM-RS). (Formula presented.) We derive the mathematical expression of MCM-RS for univariate continuous distributions and prove its uniqueness. However, for bivariate normal distribution, exact MCM-RS do not exist, prompting us to introduce two types of approximate MCM-RS and provide their computational algorithms. (Formula presented.) Simulations demonstrate that resampling using MCM-RS outperforms other sampling techniques in representativeness and excels in numerical integration, achieving high accuracy in expectation estimation.