1997/11/20 by С. И. Блинников, S. Blinnikov, Richhild Moessner +1 · 4 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Applied mathematics #Asymptotic expansion #Convergence (economics) #Edgeworth series #Gauss #Gaussian #Geophysics and Gravity Measurements #Hermite polynomials #Mathematical analysis #Mathematics #Orthogonal polynomials #Physics #Quantum mechanics #Series (stratigraphy) #Series expansion #Statistical and numerical algorithms #Statistical physics #astro-ph
paper · pdf · doi:10.1051/aas:1998221
published as Astron.Astrophys.Suppl.Ser. 130 (1998) 193-205 · 13 pages with 11 eps figures, aa.cls + graphics packages, Submitted to Astronomy & Astrophysics Supplement on July 16, 1997, accepted November 10, 1997
arxiv created 1997/11/20 · openalex publication_date 1998/05/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Various types of expansions in series of Cheby shev-Hermite polynomials currently used in astrophysics for weakly non-normal distributions are compared, namely the Gram-Charlier, Gauss-Hermite and Edgeworth expansions. It is shown that the Gram-Charlier series is most suspect because of its poor convergence properties. The Gauss-Hermite 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.