Some New Applications of P-P Plots
The P-P plot is a powerful graphical tool to compare stochastically the magnitudes of two random variables. In this note, we introduce a new partial order, called P-P order based on P-P plots. For a pair of random variables (X₁; Y₁) and (X₂; Y₂) one can see the relative precedence of Y₂ over X₂ versus that of Y₁ over X₁ using P-P order. We show that several seemingly very technical and difficult concepts like convex transform order and super-additive ordering can be easily explained with the help of this new partial order. Several concepts of positive dependence can also be expressed in terms of P-P orders of the conditional distributions.