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

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.

13 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1605.00189

References in corpus (3)

• A contraction principle in semimetric spaces
• Exploiting the Quantile Optimality Ratio to Obtain Better Confidence Intervals for Quantiles
• The Shapes of Things to Come: Probability Density Quantiles

Cited by in corpus (1)

• Evidence for goodness of fit in Karl Pearson chi-squared statistics