Some Properties of Symmetric Stable Distributions Close to the Normal Distribution

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Previous article Next article Some Properties of Symmetric Stable Distributions Close to the Normal DistributionA. V. Nagaev and S. M. Shkol’nikA. V. Nagaev and S. M. Shkol’nikhttps://doi.org/10.1137/1133014PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] W. H. DuMouchel, Stable distributions in statistical inference. II. Information from stably distributed samples, J. Amer. Statist. Assoc., 70 (1975), 386–393 51:14360 0321.62017 CrossrefGoogle Scholar[2] William H. DuMouchel, Estimating the stable index $\alpha$ in order to measure tail thickness: a critique, Ann. Statist., 11 (1983), 1019–1031 87j:62053 0547.62022 CrossrefGoogle Scholar[3] V. M. Zolotarev, One-dimensional stable distributions, Translations of Mathematical Monographs, Vol. 65, American Mathematical Society, Providence, RI, 1986x+284 87k:60002 0589.60015 CrossrefGoogle Scholar[4] M. Abramowitz and , I. A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, Vol. 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964xiv+1046 29:4914 0171.38503 Google Scholar[5] I. A. Ibragimov and , Yu. V. Linnik, Independent and stationary sequences of random variables, Wolters-Noordhoff Publishing, Groningen, 1971, 443– 48:1287 0219.60027 Google Scholar[6] A. P. Prudnikov, , Yu. A. Brychkov and , O. I. Marichev, Integrals and Series, Nauka, Moscow, 1981, (In Russian.) 0511.00044 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Asymptotics of maximum likelihood estimation for stable law with continuous parameterizationCommunications in Statistics - Theory and Methods, Vol. 50, No. 15 | 23 January 2020 Cross Ref Some Improvements in Numerical Evaluation of Symmetric Stable Density and Its DerivativesCommunications in Statistics - Theory and Methods, Vol. 35, No. 1 | 1 Feb 2006 Cross Ref Robust decorrelating decision-feedback multiuser detection in non-Gaussian channelsSignal Processing, Vol. 81, No. 9 | 1 Sep 2001 Cross Ref Recent results in applications and processing of α-stable-distributed time seriesJournal of the Franklin Institute, Vol. 333, No. 4 | 1 Jul 1996 Cross Ref Asymptotic properties of symmetric stable distributions with small indexJournal of Mathematical Sciences, Vol. 76, No. 2 | 1 Aug 1995 Cross Ref The Suzdal International Seminar of 1991 on Stability Problems for Stochastic ModelsTheory of Probability & Its Applications, Vol. 36, No. 4 | 17 July 2006AbstractPDF (5581 KB)BibliographyChance and Stability Cross Ref Volume 33, Issue 1| 1989Theory of Probability & Its Applications1-205 History Submitted:27 October 1986Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1133014Article page range:pp. 139-144ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics