EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 80(94), pp. 29–46 (2006)

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A. Baltrunas, E. Omey, and S. Van Gulck

Institute of Mathematics and Informatics, Vilnius, Lithuania and EHSAL, Stormstraat 2, 1000 Brussels, Belgium

Abstract: A distribution function $F$ on the nonnegative halfline is called subexponential if $\lim_{x\to \infty}(1-F^{*n}(x))/(1-F(x))=n$ for all $n\geq 2$. We obtain new sufficient conditions for subexponential distributions and related classes of distribution functions. Our results are formulated in terms of the hazard rate. We also analyse the rate of convergence in the definition and discuss the asymptotic behaviour of the remainder term $R_n(x)=1-F^{*n}(x)-n(1-F(x))$. We use the results in studying subordinated distributions and we conclude the paper with some multivariate extensions of our results.

Keywords: regular variation, O-regular variation, univariate and multivariate subexponential distributions, hazard rate, subordination

Classification (MSC2000): 60E99; 60G50; 26A12

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Electronic fulltext finalized on: 10 Oct 2006. This page was last modified: 4 Dec 2006.

© 2006 Mathematical Institute of the Serbian Academy of Science and Arts
© 2006 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition