Nonparametric Density Estimator
Nonparametric Density Estimator estimates the probability density of a dataset using kernel density estimation (KDE) with a Gaussian kernel. Enter a dataset (comma-separated numbers, e.g., “1,2,2.5,3”), bandwidth \\( h \\), and evaluation range \\( [a, b] \\). The calculator computes the density estimate, shows steps with MathJax, and visualizes the density curve and data points with p5.js.
Nonparametric Density Estimator
This calculator estimates the probability density of a dataset using kernel density estimation (KDE) with a Gaussian kernel. Input a dataset of numbers, bandwidth \\( h \\), and evaluation range \\( [a, b] \\). The density is estimated as \\( \hat{f}(x) = \frac{1}{nh} \sum_{i=1}^n K\left(\frac{x – x_i}{h}\right) \\), where \\( K \\) is the Gaussian kernel. Computational steps are shown with MathJax, and the density curve and data points are visualized with p5.js.
Example 1: Small Dataset
Dataset: \\( 1, 2, 2.5, 3 \\), Bandwidth: \\( h = 0.5 \\), Range: \\( [0, 4] \\).
Result: Density estimate at \\( x = 2 \approx 0.3 \\).
Example 2: Larger Dataset
Dataset: \\( 0, 0.5, 1, 1.5, 2, 2.5 \\), Bandwidth: \\( h = 0.4 \\), Range: \\( [-1, 3] \\).
Result: Density estimate at \\( x = 1 \approx 0.45 \\).