Generalized Inverse CDF Visualization
Understanding F⁻(u) = inf{x ∈ ℝ : F(x) ≥ u}
What is the Generalized Inverse CDF?
The generalized inverse CDF (quantile function) finds the smallest x value where the CDF reaches or exceeds a given probability u.
F⁻(u) = inf{x : F(x) ≥ u}
This definition works for ALL distributions: continuous, discrete, or mixed!
Current values: u = 0.50,
F⁻(u) = 0.00
How to read this visualization:
- Left plot (CDF): Shows F(x) with a horizontal line at height u. The vertical line shows where this intersects or exceeds F(x).
- Right plot (Inverse CDF): Shows F⁻(u) directly. The current u value is marked with a vertical line.
- For continuous distributions: F⁻(u) is simply where F(x) = u.
- For discrete distributions: F⁻(u) finds the smallest x where F(x) ≥ u (notice the jumps!).
- Move the slider or hover over either plot to see how u and F⁻(u) relate!