Annals of Statistics

Some inequalities for symmetric convex sets with applications

T. W. Anderson

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Under appropriate conditions the probability of a convex symmetric set decreases as the spread or scatter of the distribution increases. This paper studies the conditions when the random vector has a symmetric unimodal distribution.

Article information

Ann. Statist., Volume 24, Number 2 (1996), 753-762.

First available in Project Euclid: 24 September 2002

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Zentralblatt MATH identifier

Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60E15: Inequalities; stochastic orderings 62H15: Hypothesis testing

Convex sets inequalities unimodal functions elliptically contoured distributions monotonicity of power functions


Anderson, T. W. Some inequalities for symmetric convex sets with applications. Ann. Statist. 24 (1996), no. 2, 753--762. doi:10.1214/aos/1032894463.

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