Domains of attraction to Tweedie distributions

被引：11

作者：

Jorgensen, B. ^{[1
]}

Martinez, J. R. ^{[2
]}

Vinogradov, V. ^{[3
]}

机构：

[1] Univ So Denmark, Dept Math & Comp Sci, DK-5230 Odense M, Denmark

[2] Univ Nacl Cordoba, FAMAF, RA-5000 Cordoba, Argentina

[3] Ohio Univ, Dept Math, Athens, OH 45701 USA

来源：

LITHUANIAN MATHEMATICAL JOURNAL | 2009年 / 49卷 / 04期

关键词：

Esscher transform; exponential tilting; natural exponential family; power-variance function; Tauber theory; Tweedie domains of attraction; MODELS;

D O I：

10.1007/s10986-009-9062-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We derive new Tauberian theorems for natural exponential families, characterizing regularity properties of the family's variance function in terms of those of an extreme generating measure. This provides normal and general domains of attraction to Tweedie distributions and leads to new results on weak convergence of natural exponential families to Tweedie distributions, parallel to weak convergence toward stable laws. In particular, we give the domains of attraction to the gamma and compound Poisson-gamma distributions.

引用

页码：399 / 425

页数：27

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