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arXiv · 1701.04921

Divergence from, and Convergence to, Uniformity of Probability Density Quantiles

Robert Staudte·Aihua Xia
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Abstract

The probability density quantile (pdQ) carries essential information regarding shape and tail behavior of a location-scale family. Convergence of repeated applications of the pdQ mapping to the uniform distribution is investigated and new fixed point theorems are established. The Kullback-Leibler divergences from uniformity of these pdQs are mapped and found to be ingredients in power functions of optimal tests for uniformity against alternative shapes.

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Robert Staudte, Aihua Xia. 2017-01-18. Divergence from, and Convergence to, Uniformity of Probability Density Quantiles. https://doi.org/10.3390/e20050317

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