Metrika

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A complete characterization of bivariate densities using the conditional percentile function

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Abstract

It is well known that joint bivariate densities cannot always be characterized by the corresponding two conditional densities. Hence, additional requirements have to be imposed. In the form of a conjecture, Arnold et al. (J Multivar Anal 99:1383–1392, 2008) suggested using any one of the two conditional densities and replacing the other one by the corresponding conditional percentile function. In this article we establish, in affirmative, this conjecture and provide several illustrative examples.

Keywords

Bivariate distribution Conditional density Conditional percentile Characterization 

Mathematics Subject Classification

60E05 62E10 62H05 

Notes

Compliance with ethical standards

Conflict of interest

The corresponding author states that there is no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of North Carolina at WilmingtonWilmingtonUSA

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