Probability in the Engineering and Informational Sciences
Random variables -- Statistical methods, Stochastic analysis, Mathematical analysis
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 (X 1, Y1) and (X 2, Y 2) one can see the relative precedence of Y 2 over X 2 versus that of Y 1 over X 1 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.
Dewan, I. and Kochar, S. (2013). Some new applications of P-P plots. Probability in the Engineering and Informational Sciences, available on CJO2013.