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view Abstract Citations (96) References (19) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Higher Order Statistics of the Galaxy Distribution Using Generating Functions Szapudi, Istvan ; Szalay, Alexander S. Abstract In this paper we lay the groundwork and develop a formalism for subsequent analyses of the higher order statistics of the galaxy distribution in various catalogs, applying the method of generating functions. The generating function of the distribution is connected to the continuum limit characteristic function. The continuum moments are replaced by the factorial moments of the discrete distribution during the transition to the discrete. The generating function of the distribution is related to the generating function of other relevant quantities like the QN_'s describing the hierarchy of correlation functions, the moments, and factorial moments, and the combinants, a new and natural statistic to characterize the distribution. We calculate the probability distribution of projected cell counts and show that it uniquely translates into the projection of the N-point correlation functions via Limber's equation. Most of our results can be generalized for the connected N-point distributions as well. We introduce generating functions for the cumulative distributions which are particularly important for the cluster correlation functions. We give a collection of formulae of widely used special probability densities with their discrete counterparts and expansions of some generating functions. With the availability of efficient computer algebra programs, like MATHEMATICA, these formulae provide a true simplification. Publication: The Astrophysical Journal Pub Date: May 1993 DOI: 10. 1086/172568 Bibcode: 1993ApJ. . . 408. . . 43S Keywords: Galactic Clusters; Galaxies; Probability Distribution Functions; Spatial Distribution; Universe; Astronomical Models; Statistical Analysis; Astrophysics; COSMOLOGY: LARGE-SCALE STRUCTURE OF UNIVERSE; METHODS: NUMERICAL full text sources ADS |
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