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Beyond the Efron-Buchta identities: distributional results for Poisson polytopes by Beermann, Mareen; Reitzner, Matthias is a scholarly article available to read on EtoBox.

What is Beyond the Efron-Buchta identities: distributional results for Poisson polytopes about?

Let $\Pi$ be a random polytope defined as the convex hull of the points of a Poisson point process. Identities involving the moment generating function of the measure of $\Pi$, the number of vertices of $\Pi$ and the number of non-vertices of $\Pi$ are proven. Equivalently, identities for higher moments of the mentioned random variables are given. This generalizes analogous identities for functionals of convex hulls of i.i.d points by Efron and Buchta.

Author

Beermann, Mareen; Reitzner, Matthias

Published

2014

Language

EN