Probabilistic Properties of Bilinear Expansions of Hermite Polynomials
1967; Society for Industrial and Applied Mathematics; Volume: 12; Issue: 3 Linguagem: Inglês
10.1137/1112056
ISSN1095-7219
AutoresO. V. Sarmanov, Z. N. Bratoeva,
Tópico(s)Advanced Computational Techniques in Science and Engineering
ResumoPrevious article Next article Probabilistic Properties of Bilinear Expansions of Hermite PolynomialsO. V. Sarmanov and Z. N. BratoevaO. V. Sarmanov and Z. N. Bratoevahttps://doi.org/10.1137/1112056PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] O. V. Sarmanov, Some analytical problems important in probability theory, Trudy. IV Nauch. Konf. Matem. Kaf. Pedalog. In-tov Yuga RSFSR, Stavropol', 1963, 61–72, (In Russian.) Google Scholar[2] H. O. Lancaster, The structure of bivariate distributions, Ann. Math. Statist., 29 (1958), 719–736 MR0102150 0086.35102 CrossrefGoogle Scholar[3] H. O. Lancaster, Correlations and canonical forms of bivariate distributions, Ann. Math. Statist., 34 (1963), 532–538 MR0146912 0115.14104 CrossrefGoogle Scholar[4] O. V. Sarmanov, Pseudonormal correlation and its various generalizations, Soviet Math. Dokl., 1 (1960), 564–567 MR0121846 0095.33201 Google Scholar[5] O. S. Beryland, , R. I. Gavrilova and , A. P. Prudnikov, Tables of integral error functions and Hermite polynomials, Translated by Prasenjit Basu. A Pergamon Press Book, The Macmillan Co., New York, 1962vi+163, Oxford MR0156004 0105.11304 Google Scholar[6] V. I. Smirnov, A course of higher mathematics. Vol. III. Part two. Complex variables. Special functions, Translated by D. E. Brown. Translation edited by I. N. Sneddon, Pergamon Press, Oxford, 1964x+700 MR0182690 0118.28402 Google Scholar[7] Maurice Fréchet, Sur les tableaux de corrélation dont les marges sont données, Ann. Univ. Lyon. Sect. A. (3), 14 (1951), 53–77 MR0049518 0045.22905 Google Scholar[8] Edwin F. Beckenbach and , Richard Bellman, Inequalities, Second revised printing. Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge, Band 30, Springer-Verlag, New York, Inc., 1965xi+198 MR0192009 0126.28002 CrossrefGoogle Scholar[9] O. V. Sarmanov, Generalized normal correlation and two-dimensional Fréchet classes, Soviet Math. Dokl., 7 (1966), 596–599 Google Scholar[10] I. P. Natanson, Constructive Function Theory, Ungar, New York, 1965 Google Scholar[11] O. V. Sarmanov, The maximum correlation coefficient (symmetric case), Dokl. Akad. Nauk SSSR, 120 (1958), 715–718, (In Russian.) MR0103566 0089.36102 Google Scholar[12] O. V. Sarmanov, On monotonic solutions of correlation integral equations, Doklady AN SSSR 53, (1946), 781–784, (In Russian.) Google Scholar[13] M. K. Nomokonov, On the simpleness of the second characteristic value of correlation integral equations, Doklady Akad. Nauk SSSR (N.S.), 72 (1950), 1021–1024, (In Russian.) MR0045300 Google Scholar[14] I. S. Gradshteyn and , I. M. Ryzhik, Table of integrals, series, and products, Fourth edition prepared by Ju. V. Geronimus and M. Ju. Cei˘tlin. Translated from the Russian by Scripta Technica, Inc. Translation edited by Alan Jeffrey, Academic Press, New York, 1965xlv+1086 MR0197789 Google Scholar[15] Emile J. Gumbel, Distributions à plusieurs variables dont les marges sont données, C. R. Acad. Sci. Paris, 246 (1958), 2717–2719 MR0099728 0084.35803 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Encyclopedia of Special Functions: The Askey-Bateman Project14 September 2020 Cross Ref IFAC-PapersOnLine, Vol. 52, No. 14 | 2019 Cross Ref The Anisotropic Norm of Random Vectors: Defining via a Symmetric Tsallis Divergence2018 IEEE Conference on Control Technology and Applications (CCTA) | 1 Aug 2018 Cross Ref Application of consistent measures of dependence within fault detection and isolation problems2017 12th IEEE Conference on Industrial Electronics and Applications (ICIEA) | 1 Jun 2017 Cross Ref Distance correlation coefficients for Lancaster distributionsJournal of Multivariate Analysis, Vol. 154 | 1 Feb 2017 Cross Ref Lancaster distributions and Markov chains with multivariate Poisson–Charlier, Meixner and Hermite–Chebycheff polynomial eigenfunctionsJournal of Approximation Theory, Vol. 207 | 1 Jul 2016 Cross Ref Analytic properties of complex Hermite polynomialsTransactions of the American Mathematical Society, Vol. 368, No. 2 | 11 June 2015 Cross Ref Quantum mechanics without potential functionJournal of Mathematical Physics, Vol. 56, No. 7 | 1 Jul 2015 Cross Ref EXCHANGEABLE PAIRS OF BERNOULLI RANDOM VARIABLES, KRAWTCHOUCK POLYNOMIALS, AND EHRENFEST URNSAustralian & New Zealand Journal of Statistics, Vol. 54, No. 1 | 4 May 2012 Cross Ref Formalization and Extension of Statistical Linearization TechniquesIFAC Proceedings Volumes, Vol. 44, No. 1 | 1 Jan 2011 Cross Ref Stochastic processes with orthogonal polynomial eigenfunctionsJournal of Computational and Applied Mathematics, Vol. 233, No. 3 | 1 Dec 2009 Cross Ref Comment: Lancaster Probabilities and Gibbs SamplingStatistical Science, Vol. 23, No. 2 | 1 May 2008 Cross Ref Maximal Correlation Applied to the Statistical Linearization: An Analysis and ApproachesIFAC Proceedings Volumes, Vol. 40, No. 13 | 1 Jan 2007 Cross Ref An Identification Algorithmic Toolkit for Intelligent Control SystemsComputer Aided Systems Theory - EUROCAST'99 | 1 Jan 2000 Cross Ref Lancaster bivariate probability distributions with Poisson, negative binomial and gamma marginsTest, Vol. 7, No. 1 | 1 Jun 1998 Cross Ref The Lancaster's Probabilities on R2 and Their Extreme PointsDistributions with given Marginals and Moment Problems | 1 Jan 1997 Cross Ref The diagonal multivariate natural exponential families and their classificationJournal of Theoretical Probability, Vol. 7, No. 4 | 1 October 1994 Cross Ref On Gaussian-like densities of order greater than twoJournal of the Franklin Institute, Vol. 324, No. 3 | 1 Jan 1987 Cross Ref Optimum detection of a weak signal with minimal knowledge of dependencyIEEE Transactions on Information Theory, Vol. 32, No. 1 | 1 Jan 1986 Cross Ref On the prehistory of Correspondence AnalysisStatistica Neerlandica, Vol. 37, No. 4 | 1 Dec 1983 Cross Ref A Note on the Characterization of Bivariate Densities with Gaussian Marginal DensitiesSIAM Journal on Applied Mathematics, Vol. 37, No. 2 | 12 July 2006AbstractPDF (196 KB)Bivariate Densities with Diagonal Expansions in Gegenbauer PolynomialsJournal of the Franklin Institute, Vol. 304, No. 6 | 1 Dec 1977 Cross Ref The canonical decomposition of bivariate distributionsJournal of Multivariate Analysis, Vol. 6, No. 4 | 1 Dec 1976 Cross Ref Characterization of a class of bivariate distribution functionsJournal of Multivariate Analysis, Vol. 5, No. 2 | 1 Jun 1975 Cross Ref A Note on Positive Dependence and the Structure of Bivariate DistributionsSIAM Journal on Applied Mathematics, Vol. 20, No. 4 | 12 July 2006AbstractPDF (429 KB)On a mean-square approximation problem (Corresp.)IEEE Transactions on Information Theory, Vol. 16, No. 6 | 1 Nov 1970 Cross Ref Mildly formalized system identification based on consistent measures of dependenceIMTC/99. Proceedings of the 16th IEEE Instrumentation and Measurement Technology Conference (Cat. No.99CH36309) Cross Ref Volume 12, Issue 3| 1967Theory of Probability & Its Applications347-533 History Submitted:06 September 1965Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1112056Article page range:pp. 470-481ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics
Referência(s)