Beyond the Efron-Buchta identities: distributional results for Poisson polytopes

Mareen Beermann; Matthias Reitzner

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arXiv · 1407.5792

Beyond the Efron-Buchta identities: distributional results for Poisson polytopes

Mareen Beermann·Matthias Reitzner

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Abstract

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.

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BibTeX RIS

Mareen Beermann, Matthias Reitzner. 2014-07-22. Beyond the Efron-Buchta identities: distributional results for Poisson polytopes. https://arxiv.org/abs/1407.5792

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