An asymptotic expansion for the tail of compound sums of Burr distributed random variables

被引：4

作者：

Kortschak, Dominik ^{[1
]}

Albrecher, Hansjoerg ^{[1
]}

机构：

[1] Univ Lausanne, Fac Business & Econ, Dept Actuarial Sci, UNIL Dorigny, CH-1015 Lausanne, Switzerland

来源：

STATISTICS & PROBABILITY LETTERS | 2010年 / 80卷 / 7-8期

基金：

瑞士国家科学基金会;

关键词：

CONVOLUTIONS; PROBABILITY;

D O I：

10.1016/j.spl.2009.12.018

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper we show that it is possible to write the Laplace transform of the Burr distribution as the sum of four series. This representation is then used to provide a complete asymptotic expansion of the tail of the compound sum of Burr distributed random variables. Furthermore it is shown that if the number of summands is fixed, this asymptotic expansion is actually a series expansion if evaluated at sufficiently large arguments. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：612 / 620

页数：9

共 21 条

[1] Multi-precision laplace transform inversion [J].

Abate, J ;

Valkó, PP .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2004, 60 (05) :979-993

[2]

Abramowitz M., 2013, Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables, V(eds)

[3]

ALBRECHER H, 2010, SCAND ACTUA IN PRESS

[4] On ruin probability and aggregate claim representations for Pareto claim size distributions [J].

Albrecher, Hansjoerg ;

Kortschak, Dominik .

INSURANCE MATHEMATICS & ECONOMICS, 2009, 45 (03) :362-373

[5]

[Anonymous], 1997, APPL MATH NEW YORK

[6]

[Anonymous], WILEY SERIES PROBABI

[7]

ASMUSSEN S., 2003, APPL MATH, V51

[8]

BALTRUNAS A, 1998, LIET MAT RINK, V38, P1

[9] Asymptotic expansions of convolutions of regularly varying distributions [J].

Barbe, P ;

Mccormick, WP .

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2005, 78 :339-371

[10]

Barbe P., 2009, ASYMPTOTIC EXPANSION

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