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Second order subexponential distributions

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  09 April 2009

J. L. Geluk  and
A. G. Pakes
J. L. Geluk
Affiliation:
Erasmus University Econometric InstituteP.O. Box 1738 3000 DR Rotterdam The Netherlands
A. G. Pakes
Affiliation:
University of Western AustraliaNedlands, WA 6009, Australia
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Abstract

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The class of subexponential distributions S is characterized by F(0) = 0, 1 − F(2)(x) ~ 2(1 − F(x)) as x → ∞. In this paper we consider a subclass of S for which the relation 1 − F(2)(x) − 2(1 − F(x)) + (1 − F(x))2 = o(a(x)) as x → ∞ holds, where α is a positive function satisfying α(X) = 0(1 − F(x)) (x → ∞).

MSC classification

Secondary: 60E05: Distributions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 51 , Issue 1 , August 1991 , pp. 73 - 87
Copyright
Copyright © Australian Mathematical Society 1991

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