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SOME NEW APPLICATIONS OF P–P PLOTS

Published online by Cambridge University Press:  28 March 2013

Isha Dewan  and
Subhash Kochar
Isha Dewan
Affiliation:
Indian Statistical Institute, New Delhi, India E-mail: [email protected]
Subhash Kochar
Affiliation:
Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR E-mail: [email protected]
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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 (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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 3 , July 2013 , pp. 353 - 366
Copyright
Copyright © Cambridge University Press 2013 

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