#### Published In

Probability in the Engineering and Informational Sciences

#### Document Type

Article

#### Publication Date

3-28-2013

#### Subjects

Random variables -- Statistical methods, Stochastic analysis, Mathematical analysis

#### Abstract

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.

#### DOI

10.1017/S0269964813000077

#### Persistent Identifier

http://archives.pdx.edu/ds/psu/9522

#### Citation Details

Dewan, I. and Kochar, S. (2013). Some new applications of P-P plots. Probability in the Engineering and Informational Sciences, available on CJO2013.

## Description

Copyright Cambridge University Press 2013Originally published in Probability in the Engineering and Informational Sciences / Volume 27 / Issue 03 /July 2013, pp 353-366.

This Version of Record is archived with author permission.