Open Access
October, 1969 Limiting Sets and Convex Hulls of Samples from Product Measures
Lloyd Fisher
Ann. Math. Statist. 40(5): 1824-1832 (October, 1969). DOI: 10.1214/aoms/1177697395


Let $X_1, X_2, \cdots$ be a sequence of independent identically distributed random vectors in $R^n$ (Euclidean $n$-space). Let the $X_i$'s have a distribution which is a product of $n$ Borel probability measures along an orthogonal set of axes. After sampling $m$ times let $H_m$ be the convex hull of $\{X_1, \cdots, X_m\}$. All possible limiting shapes for $H_m$ are found along with necessary and sufficient conditions that the limit be obtained.


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Lloyd Fisher. "Limiting Sets and Convex Hulls of Samples from Product Measures." Ann. Math. Statist. 40 (5) 1824 - 1832, October, 1969.


Published: October, 1969
First available in Project Euclid: 27 April 2007

zbMATH: 0183.47501
MathSciNet: MR253391
Digital Object Identifier: 10.1214/aoms/1177697395

Rights: Copyright © 1969 Institute of Mathematical Statistics

Vol.40 • No. 5 • October, 1969
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