MATLAB Toolkit for Cauchy Distribution with Statistical Analysis Functions

A comprehensive MATLAB toolkit for Cauchy distribution analysis, featuring computation of statistical characteristics including probability density function (PDF), cumulative distribution function (CDF), inverse functions, expected value, variance, median, mode, kurtosis, and skewness. The toolkit implements parameter estimation algorithms using maximum likelihood estimation (MLE) for data fitting and distribution parameter optimization. Visualization functions generate distribution plots, probability plots, and fitting diagnostics using MATLAB's graphics capabilities. Key functions include cauchypdf() for probability density calculations, cauchycdf() for cumulative probabilities, and cauchyfit() for parameter estimation with convergence checks. When utilizing this toolkit, understanding the fundamental properties and application scenarios of Cauchy distribution is essential for effective data analysis and modeling, particularly for handling heavy-tailed distributions and outlier-sensitive applications.