Domains of attraction for exponential families
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.
Year of publication: |
2003
|
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Authors: | Balkema, August A. ; Klüppelberg, Claudia ; Resnick, Sidney I. |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 107.2003, 1, p. 83-103
|
Publisher: |
Elsevier |
Keywords: | Asymptotic normality Convex conjugate Domain of attraction Exponential family Esscher transform Gamma distribution Laplace transform Normal distribution Regular variation Self-neglecting Strongly unimodal |
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