TL;DR
This paper explores a symmetry relation between the quantiles of a random variable and its negative, revealing new properties and transformations that deepen understanding of quantile behavior.
Contribution
It introduces a novel symmetry relation for quantiles and demonstrates its usefulness in deriving new properties and equivariance under decreasing transformations.
Findings
Established a symmetry relation between quantiles of a variable and its negative.
Derived an equivariance property for quantiles under continuous decreasing transformations.
Provided insights that could influence statistical analysis involving quantiles.
Abstract
This paper finds a symmetry relation (between quantiles of a random variable and its negative) that is intuitively appealing. We show this symmetry is quite useful in finding new relations for quantiles, in particular an equivariance property for quantiles under continuous decreasing transformations.
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Taxonomy
TopicsAdvanced Control Systems Optimization · Reservoir Engineering and Simulation Methods · Computability, Logic, AI Algorithms