Plotting and Analysis of Three Major Probability Distributions: t, F, and Chi-Square

In this documentation, we present a MATLAB program designed to plot three fundamental probability distributions: t-distribution, F-distribution, and chi-square distribution. The program generates distribution curves under different parameter configurations using MATLAB's built-in statistical functions (such as tpdf, fpdf, and chi2pdf) to visualize how parameters influence distribution characteristics. We will discuss the fundamental concepts and properties of these probability distributions to provide deeper insights into their statistical applications. The implementation includes parameter variation techniques where degrees of freedom parameters are systematically modified to demonstrate their impact on distribution shape, skewness, and kurtosis. Furthermore, we explore practical applications of these distributions in statistical analysis using MATLAB, including hypothesis testing scenarios and confidence interval calculations. The code incorporates plotting best practices with proper axis labeling, legend implementation, and comparative visualization techniques. Finally, we provide real-world application examples and case studies for reference, demonstrating how to interpret the graphical output for statistical decision-making.