On the density of nonlinear statistics
Nguyen Tien Dung
TL;DR
This paper revisits the classical problem of the density of nonlinear statistics, providing a new representation of densities and establishing a necessary and sufficient condition for their existence.
Contribution
It introduces a novel density representation and the first necessary and sufficient condition for the existence of densities of nonlinear statistics.
Findings
New density representation for nonlinear statistics
Necessary and sufficient condition for density existence
Enhanced understanding of nonlinear statistic distributions
Abstract
In this note, we revisit a classical problem related to the density of nonlinear statistics. We obtain a new representation of densities and, for the first time, a necessary and sufficient condition for the existence of densities is provided.
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Taxonomy
TopicsProbability and Risk Models · Bayesian Methods and Mixture Models · Stochastic processes and statistical mechanics