I guess we want to choose the quantiles such that we sample the peaks and wings well: uniform in CDF does not seem to be optimal (or even superior to a histogram). In fact; don't we want to preferentially place interpolation nodes where the second derivative of the function is high? How about the first derivative? There must be a whole literature on this.
I guess we want to choose the quantiles such that we sample the peaks and wings well: uniform in CDF does not seem to be optimal (or even superior to a histogram). In fact; don't we want to preferentially place interpolation nodes where the second derivative of the function is high? How about the first derivative? There must be a whole literature on this.