MATLAB Code Implementation for Mathematical Statistics Applications

This collection of MATLAB programs focuses on mathematical statistics applications. The suite covers multiple important topics including Support Vector Machines (SVM) and Gaussian Mixture Models (GMM), providing robust implementations with customizable parameters. For Support Vector Machines, the programs offer comprehensive classification and regression capabilities using both linear and kernel methods (RBF, polynomial), featuring functions for data normalization, cross-validation, and model evaluation metrics like accuracy and RMSE. The implementation includes optimization algorithms for finding optimal hyperplanes and handling both separable and non-separable datasets. Regarding Gaussian Mixture Models, the code provides Expectation-Maximization (EM) algorithm implementations for cluster analysis and pattern recognition tasks. Key functions include parameter initialization, probability density calculation, and cluster assignment with Bayesian information criterion (BIC) for model selection. Additionally, the programs contain extensive mathematical statistics functions and tools for data preprocessing (handling missing values, outlier detection), probability computations (distribution fitting, hypothesis testing), and statistical inference (confidence intervals, ANOVA). The code structure emphasizes modular design with clear input/output interfaces and visualization components for result interpretation. This represents a powerful and comprehensive mathematical statistics toolkit suitable for various application domains and research projects, featuring commented code, example datasets, and performance optimization techniques for large-scale data processing.