Predict True Distribution from a Part of Gaussian Distribution

Abstract

This paper tackles the challenge of predicting dataset properties from a Gaussian-distributed subset, a key issue in statistical analysis and data science. The objective is to estimate the expected value and standard deviation of a comprehensive dataset with solely a subset. The methodology includes hypothesis testing, confidence interval estimation, regression analysis, Bayesian inference, and simulation methods. The study employs statistical models like linear and non-linear regression and Bayesian updating for prediction refinement. Resampling techniques such as bootstrapping and Monte Carlo simulations are used to ensure prediction reliability. By giving the smallest 50 GPA data in the 200 GPA data, the results show the methods’ effectiveness in predicting dataset parameters, with detailed calculations indicating the expected value likely falls between 4.073 and 4.173, and variance between 0.098 and 0.540. The precision and dependability of these predictions are emphasized in the study’s results, providing a strong basis for additional statistical investigation. Because it offers a thorough methodology for estimating population parameters from small samples, this research is significant for statistics and data analysis. Its findings are valuable in educational research, finance, and other fields dealing with incomplete or skewed data. The paper also highlights the importance of understanding statistical prediction limitations and uncertainties, offering a robust framework for future research and applications.