Domains of attraction for exponential families

August A. Balkema, Claudia Klüppelberg and Sidney I. Resnick

Stochastic Processes and their Applications, 2003, vol. 107, issue 1, 83-103

Abstract: With the df F of the rv X we associate the natural exponential family of df's F[lambda] wheredF[lambda](x)=e[lambda]x dF(x)/Ee[lambda]Xfor . Assume [lambda][infinity]=sup [Lambda][less-than-or-equals, slant][infinity] does not lie in [Lambda]. Let [lambda][short up arrow][lambda][infinity], then non-degenerate limit laws for the normalised distributions F[lambda](a[lambda]x+b[lambda]) are the normal and gamma distributions. Their domains of attractions are determined. Applications to saddlepoint and gamma approximations are considered.

Keywords: Asymptotic; normality; Convex; conjugate; Domain; of; attraction; Exponential; family; Esscher; transform; Gamma; distribution; Laplace; transform; Normal; distribution; Regular; variation; Self-neglecting; Strongly; unimodal (search for similar items in EconPapers)
Date: 2003
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4149(03)00060-7
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:107:y:2003:i:1:p:83-103

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().