Expansions for nearly Gaussian distributions
Abstract
Various types of expansions in series of ChebyshevHermite polynomials currently used in astrophysics for weakly nonnormal distributions are compared, namely the GramCharlier, GaussHermite and Edgeworth expansions. It is shown that the GramCharlier series is most suspect because of its poor convergence properties. The GaussHermite expansion is better but it has no intrinsic measure of accuracy. The best results are achieved with the asymptotic Edgeworth expansion. We draw attention to the form of this expansion found by Petrov for arbitrary order of the asymptotic parameter and present a simple algorithm realizing Petrov's prescription for the Edgeworth expansion. The results are illustrated by examples similar to the problems arising when fitting spectral line profiles of galaxies, supernovae, or other stars, and for the case of approximating the probability distribution of peculiar velocities in the cosmic string model of structure formation.
 Publication:

Astronomy and Astrophysics Supplement Series
 Pub Date:
 May 1998
 DOI:
 10.1051/aas:1998221
 arXiv:
 arXiv:astroph/9711239
 Bibcode:
 1998A&AS..130..193B
 Keywords:

 METHODS: STATISTICAL;
 COSMIC STRINGS;
 LINE: PROFILES;
 Astrophysics
 EPrint:
 13 pages with 11 eps figures, aa.cls + graphics packages, Submitted to Astronomy &