S. Blinnikov, and R. Moessner. (1997)cite arxiv:astro-ph/9711239Comment: 13 pages with 11 eps figures, aa.cls + graphics packages, Submitted to Astronomy & Astrophysics Supplement on July 16, 1997, accepted November 10, 1997.
DOI: 10.1051/aas:1998221
Abstract
Various types of expansions in series of Chebyshev-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.
%0 Generic
%1 blinnikov1997expansions
%A Blinnikov, S.
%A Moessner, R.
%D 1997
%K cornishfisher distributions edgeworth gram-charlier
%R 10.1051/aas:1998221
%T Expansions for nearly Gaussian distributions
%U http://arxiv.org/abs/astro-ph/9711239
%X Various types of expansions in series of Chebyshev-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.
@misc{blinnikov1997expansions,
abstract = {Various types of expansions in series of Chebyshev-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.},
added-at = {2015-02-20T19:58:37.000+0100},
author = {Blinnikov, S. and Moessner, R.},
biburl = {https://www.bibsonomy.org/bibtex/267efe454d425a80e1f403c70e4375e2c/shabbychef},
description = {Expansions for nearly Gaussian distributions},
doi = {10.1051/aas:1998221},
interhash = {307b38fef65fc4dde8ffb58c476d900c},
intrahash = {67efe454d425a80e1f403c70e4375e2c},
keywords = {cornishfisher distributions edgeworth gram-charlier},
note = {cite arxiv:astro-ph/9711239Comment: 13 pages with 11 eps figures, aa.cls + graphics packages, Submitted to Astronomy & Astrophysics Supplement on July 16, 1997, accepted November 10, 1997},
timestamp = {2015-02-20T19:58:37.000+0100},
title = {Expansions for nearly Gaussian distributions},
url = {http://arxiv.org/abs/astro-ph/9711239},
year = 1997
}