AVERAGED_INVERTED_CDF

Averaged inverse of the empirical CDF (HF2, R type 2).

Same as INVERTED_CDF but averages the two bracketing order statistics at discontinuity points. This smooths the step function of HF1 at its jump points.

Note: at q = 0, this returns the average of x0 and x1 (not the minimum), because q = 0 is itself a discontinuity point. This differs from all other methods, which return x0 at q = 0.