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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Multivariate probability inequalities
TL;DR: Several important multivariate probability inequalities can be formulated in terms of multivariate convolutions of the form f fi(x)f2(x??)??, where usually /i = Ic is the indicator of a region C? IRn, ji is a probability density on Hn, and? is a translation parameter as discussed by the authors.
Dissertation
Equivalence testing for mean vectors of multivariate normal populations
TL;DR: Thesis (Ph.D.) as discussed by the authors, WSU, College of Liberal Arts and Sciences, Dept. of Mathematics and Statistics, Wichita State University, WSU College of Business and Management
Journal ArticleDOI
Bounds on Mahalanobis norms and their applications
TL;DR: In this article, local and global bounds for ratios of norms, and minimal and maximal norms, are constructed for pairs and ensembles of quadratic norms of R k, with corresponding results for Mahalanobis distance functions.
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$${\mathcal{M}}$$ -decomposability and symmetric unimodal densities in one dimension
Nicholas Chia,Junji Nakano +1 more
TL;DR: In this article, the notion of decomposability of probability density functions in one dimension was introduced and an inequality that applies to all symmetric unimodal densities was derived.
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.
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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].