Non-Gaussian Chi-squared method with the multivariate Edgeworth expansion

Details Non-Gaussian Chi-squared method with the multivariate Edgeworth expansion Non-Gaussian Chi-squared method with the multivariate Edgeworth expansion

1998-10-13

arxiv.org/abs/astro-ph/9810198v1

Astro. Lett. and Communications, 1996, 33, 63

Astronomy and Astrophysics

Astrophysics

7 pages, 2 figures. This is a paper published in 1996 in the proceedings of an Italian meeting. Since the proceedings are hard

Scientific paper

I present here a generalization of the maximum likelihood method and the $\chi^2$ method to the cases in which the data are {\it not} assumed to be Gaussian distributed. The method, based on the multivariate Edgeworth expansion, can find several astrophysical applications. I mention only two of them. First, in the microwave background analysis, where it cannot be excluded that the initial perturbations are non-Gaussian. Second, in the large scale structure statistics, as we already know that the galaxy distribution deviates from Gaussianity on the scales at which non-linearity is important. As a first interesting result I show here how the confidence regions are modified when non-Gaussianity is taken into account.

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