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.
Bivariate distribution Conditional density Conditional percentile Characterization
Mathematics Subject Classification
60E05 62E10 62H05
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Conflict of interest
The corresponding author states that there is no conflict of interest.
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