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On an Inequality and a Related Characterization of the Normal Distribution

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Next article On an Inequality and a Related Characterization of the Normal DistributionA. A. Borovkov and S. A. UtevA. A. Borovkov and S. A. Utevhttps://doi.org/10.1137/1128021PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] H. Chernoff, A note on an inequality involving the normal distribution, Ann. Probab., 9 (1981), 533–535 82f:60050 0457.60014 CrossrefGoogle Scholar[2] V. R. Portnov, Two embedding theorems for the space $L\sb{p,b}\sp{(1)}(\Omega \times R\sb{+})$ and their applications, Dokl. Akad. Nauk SSSR, 155 (1964), 761–764, (In Russian.) 28:4243 Google Scholar[3] F. A. Sysoeva, Generalization of a certain Hardy inequality, Izv. Vysš. Učebn. Zaved. Matematika, 1965 (1965), 140–143, (In Russian.) 33:240 Google Scholar[4] V. N. Sedov, Weighted spaces. The imbedding theorem, Differencialnye Uravnenija, 8 (1972), 1452–1462, (In Russian.) 46:9715 Google Scholar[5] A. Kufner, Imbedding theorems for general Sobolev weight spaces, Ann. Scuola Norm. Sup. Pisa (3), 23 (1969), 373–386 40:6253 0198.46205 Google Scholar[6] L. D. Kudryavtsev, Polynomial traces and moduli of smoothness of functions of several variables, Trudy Mat. Inst. Steklov., 117 (1972), 180–211, 344–345, (In Russian.) 51:13670 Google Scholar[7] A. N. Kolmogorov and , S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, Nauka, Moscow, 1976, (In Russian.) Google Scholar[8] P. Billingsley, Convergence of probability measures, John Wiley & Sons Inc., New York, 1968xii+253 38:1718 0172.21201 Google Scholar Next article FiguresRelatedReferencesCited ByDetails First-order covariance inequalities via Stein's methodBernoulli, Vol. 26, No. 3 | 1 Aug 2020 Cross Ref An anomaly based distributed detection system for DDoS attacks in Tier-2 ISP networksJournal of Ambient Intelligence and Humanized Computing, Vol. 145 | 19 June 2020 Cross Ref Bounds on the Poincaré constant for convolution measuresAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 56, No. 1 | 1 Feb 2020 Cross Ref A bound on the Wasserstein-2 distance between linear combinations of independent random variablesStochastic Processes and their Applications, Vol. 129, No. 7 | 1 Jul 2019 Cross Ref Existence of Stein kernels under a spectral gap, and discrepancy boundsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 55, No. 2 | 1 May 2019 Cross Ref On Stein's method for multivariate self-decomposable laws with finite first momentElectronic Journal of Probability, Vol. 24, No. none | 1 Jan 2019 Cross Ref Entropy and Thinning of Discrete Random VariablesConvexity and Concentration | 21 April 2017 Cross Ref Parametric Stein operators and variance boundsBrazilian Journal of Probability and Statistics, Vol. 30, No. 2 | 1 May 2016 Cross Ref A new powerful version of the BUS test of normalityStatistical Methods & Applications, Vol. 24, No. 3 | 15 November 2014 Cross Ref Variance, Upper BoundsWiley StatsRef: Statistics Reference Online | 26 November 2014 Cross Ref Bounds on the Poincaré constant under negative dependenceStatistics & Probability Letters, Vol. 83, No. 2 | 1 Feb 2013 Cross Ref Functional Properties of Minimum Mean-Square Error and Mutual InformationIEEE Transactions on Information Theory, Vol. 58, No. 3 | 1 Mar 2012 Cross Ref ReferencesExtreme Value Methods with Applications to Finance | 7 February 2012 Cross Ref Exploring the statistical applicability of the Poincaré inequality: a test of normalityTEST, Vol. 20, No. 2 | 14 July 2010 Cross Ref On Some Inequalities of Chernoff–Borovkov–Utev Type for Circular DistributionsAdvances in Directional and Linear Statistics | 27 September 2010 Cross Ref Nonlinear principal components, II: Characterization of normal distributionsJournal of Multivariate Analysis, Vol. 100, No. 4 | 1 Apr 2009 Cross Ref Some results on lower variance bounds useful in reliability modeling and estimationAnnals of the Institute of Statistical Mathematics, Vol. 60, No. 3 | 30 May 2007 Cross Ref Forecasting Probability of Precipitation Using Morkov Logistic Regression ModelCommunications for Statistical Applications and Methods, Vol. 14, No. 1 | 30 Apr 2007 Cross Ref A Note Based on Multiparameter Discrete Exponential Families in View of Cacoullos-type InequalitiesCommunications for Statistical Applications and Methods, Vol. 14, No. 1 | 30 Apr 2007 Cross Ref A new characterization of the normal lawStatistics & Probability Letters, Vol. 77, No. 1 | 1 Jan 2007 Cross Ref Variance, Upper BoundsEncyclopedia of Statistical Sciences | 15 August 2006 Cross Ref Characterization of Continuous Distributions by Variance Bound and Its Implications to Reliability Modeling and Catastrophe TheoryCommunications in Statistics - Theory and Methods, Vol. 35, No. 7 | 22 September 2006 Cross Ref A matrix variance inequalityJournal of Statistical Planning and Inference, Vol. 130, No. 1-2 | 1 Mar 2005 Cross Ref A New Method for Bounding Rates of Convergence of Empirical Spectral DistributionsJournal of Theoretical Probability, Vol. 17, No. 4 | 1 Oct 2004 Cross Ref Concentration of normalized sums and a central limit theorem for noncorrelated random variablesThe Annals of Probability, Vol. 32, No. 4 | 1 Oct 2004 Cross Ref Fisher information inequalities and the central limit theoremProbability Theory and Related Fields, Vol. 129, No. 3 | 29 April 2004 Cross Ref Convergence of the Poincaré ConstantO. 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