On closure and factorization properties of subexponential and related distributions

Autor: Charles M. Goldie, Paul Embrechts
Rok vydání: 1980
Předmět:
Zdroj: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics. 29:243-256
ISSN: 0263-6115
1446-7887
DOI: 10.1017/s1446788700021224
Popis: For a distribution function F on [0, ∞] we say F ∈ if {1 – F(2)(x)}/{1 – F(x)}→2 as x→∞, and F∈, if for some fixed γ > 0, and for each real , limx→∞ {1 – F(x + y)}/{1 – F(x)} ═ e– n. Sufficient conditions are given for the statement F ∈ F * G ∈ and when both F and G are in y it is proved that F*G∈pF + 1(1 – p) G ∈ for some (all) p ∈(0,1). The related classes ℒt are proved closed under convolutions, which implies the closure of the class of positive random variables with regularly varying tails under multiplication (of random variables). An example is given that shows to be a proper subclass of ℒ 0.
Databáze: OpenAIRE