The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities
T. W. Anderson
- Vol. 6, Iss: 2, pp 170-176
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The article was published on 1955-02-01 and is currently open access. It has received 552 citations till now. The article focuses on the topics: Convex set & Subderivative.read more
Citations
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Journal ArticleDOI
Some problems concerning centrally symmetric convex bodies
V. A. Zalgaller,V. N. Sudakov +1 more
TL;DR: In this paper, it was shown that among convex bodies Q in Rn, with a center of symmetry at the origin, for which the value of √ √ q = const, the maximum is a maximum when Q is the layer between two hyperplanes, for n = 2 and n=3.
Book ChapterDOI
Selektionsprozeduren Mit Erweitertem Entscheidungsraum
TL;DR: In this paper, klassischen, auf dem Bechhoferschen Ansatz basierenden Selektionsprozeduren erweisen sich fur viele praktische Belange, vor allen Dingen im medizinischen Bereich, in ihren Aussagemoglichkeiten haufig als zu restriktiv.
Book ChapterDOI
Some Auxiliary Results — Monotonicity Properties of Probability Distributions
Shanti S. Gupta,Deng-Yuan Huang +1 more
TL;DR: In this paper, the authors studied the monotonicity properties of distributions in order to obtain inequalities useful in statistical inference, and showed that some of these properties are well known and have proved to be very useful.
Journal ArticleDOI
Monotonicity Results for Coherent MIMO Rician Channels
TL;DR: The dependence of the Gaussian input information rate on the line-of-sight (LOS) matrix in multiple-input multiple-output coherent Rician fading channels is explored in this paper.
A phase transition in zero count probability for stationary gaussian processes
Naomi Feldheim,Ohad N. Feldheim +1 more
TL;DR: In this paper , the authors studied the probability that a real stationary Gaussian process has at least ηT zeros in [0, T ] (overcrowding), or at most this number (undercrowded) and showed that if the spectral measure of the process is supported on ± [B, A ], overcrowding probability transitions from exponential decay to Gaussian decay at η = Aπ , while undercrowdness probability undergoes the reverse transition at δ = Bπ .
References
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Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes
TL;DR: In this article, a general method for calculating the limiting distributions of these criteria is developed by reducing them to corresponding problems in stochastic processes, which in turn lead to more or less classical eigenvalue and boundary value problems for special classes of differential equations.
BookDOI
Theorie der Konvexen Körper
T. Bonnesen,W. Fenchel +1 more
TL;DR: In this article, Minkowski et al. den engen Zusammenhang dieser Begriffbildungen und Satze mit der Frage nach der bestimmung konvexer Flachen durch ihre GAusssche Krtim mung aufgedeckt und tiefliegende diesbeztigliche Satze bewiesen.
Journal ArticleDOI
The Cramer-Smirnov Test in the Parametric Case
TL;DR: In this paper, the authors extended the Cramer-Smirnov and von Mises test to the parametric case, a suggestion of Cramer [1], see also [2].