MATLAB Implementation of Monte Carlo Algorithm with Extensible Code Design

This text introduces a Monte Carlo algorithm implementation designed with self-expansion and modification capabilities. The program employs a modular architecture where core functions like random number generation, statistical analysis, and result visualization are implemented as separate modules. Key MATLAB functions include rand()/randn() for probability distribution sampling, mean()/std() for statistical processing, and plot() for result visualization. Users can extend functionality by adding new modules—for instance, implementing variance reduction techniques through antithetic variates or control variates methods. The algorithm follows standard Monte Carlo workflow: problem definition → probability modeling → random sampling → statistical estimation → convergence analysis. The open structure allows modifications like custom probability distributions using inverse transform sampling, or parallelization through parfor loops for performance optimization. This adaptability makes it suitable for diverse applications including financial risk modeling, physical system simulation, and numerical integration. The code serves as both a practical tool and educational resource, enabling users to understand Monte Carlo principles through hands-on experimentation with algorithmic parameters and implementation details.