The expected value of some functions of the convex hull of a random set of points sampled in \(\mathbb{R}{}^ d\) (Q1178331)
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scientific article; zbMATH DE number 21519
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The expected value of some functions of the convex hull of a random set of points sampled in \(\mathbb{R}{}^ d\) |
scientific article; zbMATH DE number 21519 |
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The expected value of some functions of the convex hull of a random set of points sampled in \(\mathbb{R}{}^ d\) (English)
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26 June 1992
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The author presents formulas and asymptotic expansions for the expected number of vertices and the expected volume of the convex hull of a sample of \(n\) points taken from the uniform distribution on a \(d\)-dimensional unit ball. These extend well-known results of Rényi and Sulanke for \(d=2\) and agree with formulas obtained by Efron for \(d=2,3\) and more general distributions. At the end of the paper an application to statistics is given.
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convex hull of random points
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asymptotic mean values
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asymptotic expansions
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