On the oscillation of the expected number of extreme points of a random set

Luc Devroye

Statistics & Probability Letters, 1991, vol. 11, issue 4, 281-286

Abstract: Let ENn be the expected number of extreme points among n i.i.d. points with a common radially symmetric distribution in the plane. We show that for any monotone sequence [omega]n [short up arrow] [infinity] and for every [var epsilon] > 0, there exists a radially symmetric distribution for which ENn [greater-or-equal, slanted] n/[omega]n infinitely often and ENn [less-than-or-equals, slant] 4 + [var epsilon] infinitely often. In addition, there exists a unimodal radially symmetric density such that ENn [greater-or-equal, slanted] n/[omega]n infinitely often and ENn [less-than-or-equals, slant] 4 + [var epsilon] infinitely often.

Keywords: Convex; hull; conterexamples; symmetric; distributions; stochastic; geometry (search for similar items in EconPapers)
Date: 1991
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Citations: View citations in EconPapers (3)

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