Mathematics – Probability
Scientific paper
May 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993apj...408...43s&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 408, no. 1, p. 43-56.
Mathematics
Probability
78
Galactic Clusters, Galaxies, Probability Distribution Functions, Spatial Distribution, Universe, Astronomical Models, Statistical Analysis
Scientific paper
The method of generating functions is applied in order to lay the groundwork and develop a formalism for subsequent analyses of the higher order statistics of the galaxy distribution in various catalogs. The generating function of the distribution is connected to the continuum limit characteristic function, and the continuum moments are replaced by the factorial moments of the discrete distribution during the transition to the discrete. The probability distribution of projected cell counts is calculated and it is shown that this uniquely translates into the projection of the N-point correlation functions via Limber's equation. Generating functions for the cumulative distributions which are particularly important for the cluster correlation functions are introduced. A collection of formulae of widely used special probability densities with their discrete counterparts and expansions of some generating functions are given.
Szalay Alexander S.
Szapudi István
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