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Some Notes on the Positive Lattice Long-Tailed Family(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2006年01期
Page:
30-33
Research Field:
数学
Publishing date:

Info

Title:
Some Notes on the Positive Lattice Long-Tailed Family
Author(s):
Yang Yang~
(1. Department of AppliedMathematics, Nanjing Audit University, Nanjing 210029, China)
(2. Department of Mathematics, Soochow University, Suzhou 215006, China)
Keywords:
Heavy-tailed distribution;  Long2tailed family(L ) ;  positive lattice
PACS:
O211.3
DOI:
-
Abstract:
In order to obtain some p roperties of Long-tailed family, this paper uses mathematical induc tion, gives the equivalent condition of Possion app roximation of i. i. d. r. v. s in the positive lattice Long- tailed family, hence obtains a method, which can check whether i. i. d. r. v. s in the positive lattice Long- tailed family can be Poisson app roximated. Thismethod ismore concise than that in Embrechts et al. On the other hand, we give a special p roof of the additivity of the positive lattice Long-tailed family.

References:

[ 1 ] Embrechts P, Kluppelberg C, Mikosch T. Modelling Extremal Events [M ]. Berlin: Sp ringer-Verlag, 1977.
[ 2 ] MandjesM. Overflow behavior in queueswith many long2tailed inputs [ J ]. Adv in App l Prob, 2000, 32 (4) : 1150—1167.
[ 3 ] 苏淳,胡治水,唐启鹤. 关于非负分布重尾程度的刻画[ J ]. 数学进展, 2003, 32 (5) : 606—614.
[ 4 ] Su C, Tang Q, J iang T. A contribution to large deviations for heavy2tailed random sums [ J ]. Science in China Series A: Mathematics, 2001, 44 (4) : 438—444.
[ 5 ] Tang Q, Su C, J iang T, Zhang J. Large deviations for heavy2tailed random sums in compound renewal model [ J ]. Statist and Prb Letters, 2001, 52 (1) : 91—100.

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Last Update: 2013-05-05