Nonparametric Density Estimation Using Gaussian Kernel

This program implements nonparametric density estimation using Gaussian kernels, which employs kernel density estimation with Gaussian functions to estimate probability densities from sample data. The implementation includes bandwidth estimation formulas - a critical parameter that determines the smoothness of the density estimate. Through probability density estimation on samples, we can better understand data distributions, enabling more accurate analysis and predictions. The code typically involves calculating weighted sums of Gaussian functions centered at each data point, with the bandwidth parameter controlling the kernel's width. Key implementation aspects include: computing kernel functions for each data point, optimizing bandwidth selection using rules like Silverman's rule or cross-validation, and efficiently summing contributions from all kernels. Notably, nonparametric density estimation methods don't rely on distributional assumptions, making them flexible for various data types and distribution patterns. Common applications include data visualization, outlier detection, and preparatory analysis for machine learning models.