Geodesic
Hazard Rates and Subexponential Distributions
Publications de l'Institut Mathématique, _N_S_80 (2006) no. 94, p. 29 .

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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.
DOI : 10.2298/PIM0694029B
Classification : 60E99 60G50 26A12
Keywords: regular variation, O-regular variation, univariate and multivariate subexponential distributions, hazard rate, subordination 
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     author = {A. Baltrunas and E. Omey and S Van Gulck},
     title = {Hazard {Rates} and {Subexponential} {Distributions}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {29 },
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A. Baltrunas; E. Omey; S Van Gulck. Hazard Rates and Subexponential Distributions. Publications de l'Institut Mathématique, _N_S_80 (2006) no. 94, p. 29 . doi : 10.2298/PIM0694029B. http://geodesic.mathdoc.fr/articles/10.2298/PIM0694029B/

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