A sharp Abelian theorem for the Laplace transform

2013/09/24 by Maeva Biret, Michel Broniatowski, Biret, Maeva +3
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Statistics Theory (math.ST) #math.CA #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1309.6267

To appear in M. Hallin, D. Mason, D. Pfeifer, and J. Steinebach Eds, Mathematical Statistics and Limit Theorems: Festschrift in Honor of Paul Deheuvels. Springer, 20 pages

arxiv created 2014/03/20 · arxiv updated 2014/03/21

Abstract

This paper states asymptotic equivalents for the three first moments of the Eescher transform of a distribution on R with smooth density in the upper tail. As a by product if provides a tail approximation for its moment generating function, and shows that the Esscher transforms have a Gaussian behavior for large values of the parameter.

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