IMPACT OF SAMPLE SIZE ON THE ACCURACY OF PARAMETER ESTIMATION IN VARIOUS PROBABILITY DISTRIBUTIONS

Abstract

Despite the general consensus that larger samples improve estimation accuracy, there was limited comprehensive understanding of how this relationship differed among various distributions. This study filled this gap by systematically analyzing the effect of sample size on parameter estimation accuracy. The objectives included evaluating the relationship between sample size and estimation accuracy for different distributions, comparing the performance of different estimation methods, identifying minimum sample sizes required for specified accuracy levels, and providing practical guidelines for researchers. Focusing on normal, binomial, Poisson, exponential, and gamma distributions, the study examined sample sizes ranging from small (n=10) to large (n=1000). The methodology included simulation studies to generate datasets, accuracy assessment using bias, mean squared error (MSE), and confidence intervals, and comparative analysis to identify patterns and trends. The expected outcomes included a detailed understanding of sample size effects on estimation accuracy, identification of minimum sample sizes for accurate estimation, and development of practical guidelines to enhance the efficiency and reliability of statistical analyses across various fields.