SOME NEW APPLICATIONS OF P–P PLOTS
Isha Dewan, Subhash C. Kochar · Probability in the Engineering and Informational Sciences · 2013
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 ofY2overX2versus that ofY1overX1using 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.