Ratio function vs. shift distribution

Let’s say we have two distributions \(X\) and \(Y\). In the previous post, we discussed how to express the “absolute difference” between them using the shift function and the shift distribution. Now let’s discuss how to express the “relative difference” between them. This abstract term also could be expressed in various ways. My favorite approach is to build the ratio function. In order to do this, for each quantile \(p\), we should calculate \(Q_Y(p)/Q_X(p)\) where \(Q\) is the quantile functio...