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

HAZARD RATES AND SUBEXPONENTIAL DISTRIBUTIONSA. Baltrunas, E. Omey, and S. Van GulckInstitute of Mathematics and Informatics, Vilnius, Lithuania and EHSAL, Stormstraat 2, 1000 Brussels, BelgiumAbstract: A distribution function $F$ on the nonnegative halfline is called subexponential if $\lim_{x\to \infty}(1F^{*n}(x))/(1F(x))=n$ 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 $R_n(x)=1F^{*n}(x)n(1F(x))$. We use the results in studying subordinated distributions and we conclude the paper with some multivariate extensions of our results. Keywords: regular variation, Oregular variation, univariate and multivariate subexponential distributions, hazard rate, subordination Classification (MSC2000): 60E99; 60G50; 26A12 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 10 Oct 2006. This page was last modified: 4 Dec 2006.
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