Theoretical Statistics and Mathematics Unit, ISI Delhi

Some new applications of P-P plots

by Isha Dewan and Subhash Kochar

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 $(X_1,Y_1)$ 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.

isid/ms/2012/10 [fulltext]

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