Class Probability Distributions Research Articles

An Easily Mechanized Scheme for an Adaptive Pattern Recognizer

Adaptive pattern recognizers incorporate approximations to the class probability distributions that improve as a result of cumulative information derived from known inputs. A simple method is outlined in which a stored sample constitutes a set of points in observation-space at each of which the local value of a class's distribution can be estimated cumulatively as known class-members become available. The membership of the sample representing each class is modified to fill gaps and to adjust to the relative spread of the distribution. Only a minimum of computation, mostly simple counting, is required.

About Transfer Functions with Approximately Constant Time-Delay

Adaptive pattern recognizers incorporate approximations to the class probability distributions that improve as a result of cumulative information derived from known inputs. A simple method is outlined in which a stored sample constitutes a set of points in observation-space at each of which the local value of a class's distribution can be estimated cumulatively as known class-members become available. The membership of the sample representing each class is modified to fill gaps and to adjust to the relative spread of the distribution. Only a minimum of computation, mostly simple counting, is required.

Probability Distributions of Random Variables Associated with a Structure of the Sample Space of Sociometric Investigations

In this paper, we consider a disjoint decomposition, at three levels, of the total sample space for $n$-person, one-dimensional sociometric investigations. This results in a structure particularly suited to determination of the probability distributions of a large class of sociometric variables. Systematic methods for obtaining these distributions are presented and illustrated by two examples; while the first is trivial, the second produces a previously unknown result. It should be remarked that the methods developed here have application in the theory of communication networks and, indeed, in the study of any network situations which may be represented by either of the two models employed in the paper.

A Remark on Probability Distributions of Class L

Previous article Next article A Remark on Probability Distributions of Class LI. A. IbragimovI. A. Ibragimovhttps://doi.org/10.1137/1102007PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractAn example of a non-unimodal probability distribution of class L is given.[1] B. V. Gnedenko and , A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, GITTL, Moscow-Leningrad, 1949, (In Russian.) Google Scholar[2] K. L. Chung, Sur les lois de probabilité unimodales, C. R. Acad. Sci. Paris, 236 (1953), 583–584 MR0053419 (14,771b) 0050.13702 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails A Study of One Null Array of Random Variables3 December 2013 Cross Ref Some classes generated by exponential distributions19 September 2006 Cross Ref Unimodality and Bounds of Modes for Distributions of Generalized Sojourn Times Cross Ref The Absolute Continuity of the Distribution Functions in the Class L Cross Ref On the unimodality of infinitely divisible distribution functions II22 October 2006 Cross Ref On the unimodality of infinitely divisible distribution functionsZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 45, No. 4 Cross Ref Volume 2, Issue 1| 1957Theory of Probability & Its Applications History Submitted:22 February 1957Published online:28 July 2006 InformationCopyright © 1957 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1102007Article page range:pp. 117-119ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics