Generation and Visualization Functions for 2D Gaussian Distribution Data

For generating and visualizing bivariate Gaussian distribution data, we have developed a comprehensive set of MATLAB functions that facilitate data simulation and analysis. The implementation employs random number generation algorithms to create datasets with specified mean vectors and covariance matrices, accurately capturing the elliptical distribution patterns characteristic of bivariate Gaussian data. Key functions include data generation using multivariate normal distribution algorithms and visualization tools that create contour plots and 3D surface representations. These tools allow researchers to simulate correlated datasets with controlled parameters, analyze distribution properties through statistical visualization, and test various scenarios by adjusting covariance structures. The functions incorporate efficient matrix operations for covariance decomposition and eigenvalue calculations, ensuring numerical stability during data generation. This toolkit enables analysts to study correlation effects, cluster patterns, and probability densities in bivariate systems, supporting informed decision-making through customizable simulation environments that can model real-world data behaviors with precision.