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Modern Stochastics: Theory and Applications


Integrated quantile functions: properties and applications
Volume 4, Issue 4 (2017), pp. 285–314
Pub. online: 8 December 2017      Type: Research Article      Open accessOpen Access
Received
9 August 2017
Revised
6 November 2017
Accepted
8 November 2017
Published
8 December 2017

Abstract

In this paper we provide a systematic exposition of basic properties of integrated distribution and quantile functions. We define these transforms in such a way that they characterize any probability distribution on the real line and are Fenchel conjugates of each other. We show that uniform integrability, weak convergence and tightness admit a convenient characterization in terms of integrated quantile functions. As an application we demonstrate how some basic results of the theory of comparison of binary statistical experiments can be deduced using integrated quantile functions. Finally, we extend the area of application of the Chacon–Walsh construction in the Skorokhod embedding problem.

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© 2017 The Author(s). Published by VTeX
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Keywords
Quantile functions integrated quantile functions integrated distribution functions convex stochastic order binary experiments Chacon–Walsh construction

MSC2010
60E05 62E15 60B10 26A48

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