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
Reads0
Chats0
About:
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
More filters
Journal ArticleDOI
Anomalies in the analysis of calibrated data
TL;DR: In this article, the authors examine the effects of calibration errors on model assumptions and data-analytic tools in direct calibration assays, including induced dependencies, inflated variances, and heteroscedasticity among calibrated measurements, whose distributions arise as mixtures.
Book ChapterDOI
Random Closed Sets and Capacity Functionals
TL;DR: In this paper, a random set is defined as an object with values being sets, so that the corresponding record space is the space of subsets of a given carrier space, and a simple definition of a general random element like random set presents little difficulty as soon as a σ-algebra on the record space was specified.
Posted Content
A stochastic output-feedback MPC scheme for distributed systems
Christoph Mark,Steven Liu +1 more
TL;DR: A novel stochastic outputfeedback MPC scheme for distributed systems with additive process and measurement noise is presented, and closed-loop chance constraint satisfaction, recursive feasibility and convergence to an asymptotic average cost bound are proven.
Journal ArticleDOI
Symmetry and Unimodality in Linear Inference
TL;DR: In this article, distribution-free results beyond Gauss-Markov theory are found under weak assumptions regarding the errors, including symmetry, unimodality, and location-scale families.
Book ChapterDOI
Unions of Random Sets
TL;DR: In this article, it was shown that every random variable ξ is max-infinitely divisible, i.i.d., and that ξ coincides in distribution with max(ξ1n, …, ξ nn ) for random variables ξ 1n, etc.
References
More filters
Journal ArticleDOI
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].