MATLAB Implementation for Mathematical Modeling with Normality Testing

In mathematical modeling applications, validating data normality is a critical prerequisite for many statistical analyses. This MATLAB implementation provides comprehensive normality testing capabilities through several approaches. The program utilizes key statistical functions including the Kolmogorov-Smirnov test (kstest), Lilliefors test (lillietest), and Jarque-Bera test (jbtest) to assess data distribution properties. The implementation features data preprocessing routines that handle missing values and outliers before testing. The code generates quantile-quantile (Q-Q) plots for visual assessment and calculates essential statistics like skewness and kurtosis. Users can select between parametric and non-parametric testing methods based on sample size and data characteristics. Each test returns both the test statistic and p-value, allowing for proper interpretation at common significance levels (α=0.05, α=0.01). The program includes automated reporting features that summarize test results and provide practical recommendations for subsequent modeling steps. For large datasets, the implementation incorporates efficient vectorized operations to ensure computational performance. Note that a non-significant test result indicates consistency with normal distribution rather than definitive proof of normality. The modular code structure allows easy integration with existing modeling workflows and supports batch processing for multiple datasets. This MATLAB solution represents a reliable tool for researchers and practitioners requiring rigorous normality validation in their modeling projects.