Setting the Distribution Parameters

You can control the parameters of the mean vector and the covariance matrix using sliders.

• Mean X (μ₁): Controls the center of the distribution along the X-axis.
• Mean Y (μ₂): Controls the center along the Y-axis.
• Variance X (σ₁²): Controls the spread of the distribution along X.
• Variance Y (σ₂²): Controls the spread along Y.
• Covariance (σ₁₂): Controls the tilt or orientation of the ellipse (how X and Y move together).
• Use the sliders and observe values updating in real-time next to the labels

Generating and Resetting Data

• Click “Generate Data” to sample a new distribution with the current parameters.
• Click “Reset” to return all sliders and settings to default.

Enhancing the Visualization

• Show Principal Axes: Displays eigenvectors over the ellipse.
• Show Density Contours: Adds contour lines showing density levels.

Point Interaction:

Enable “Point Dragging” to interactively move sample points and see how it affects distribution.

Using Presets

Click any of the preset buttons to auto-load commonly used parameter settings