Statistics – Computation
Scientific paper
Jun 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989apj...341..588s&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 341, June 15, 1989, p. 588-598.
Statistics
Computation
38
Computational Astrophysics, Galactic Clusters, Statistical Distributions, Gravitational Effects, Kolmogoroff Theory, Many Body Problem, Stochastic Processes, Thermodynamics
Scientific paper
Some of the mathematical and physical properties of the probability distribution f(N) which describes the observed clustering of galaxies are derived, including an exact, explicit formula for the generating function of f(N). This shows that different volumes are stochastically independent and that the form of the function applies to its two-dimensional projection on the sky as well as in three dimensions. Two different cluster decompositions of f(N) are derived, one of which is essentially the multiplicity function. Subsidiary distribution functions for extremal distributions of f(N) are derived, and the generating function is used as a simple method for determining various statistical quantities such as means and moments. Compounded, filtered, and conditional forms of the distribution function are discussed, and their relation to observational selection and physical bias is examined. A spatial Kolmogorov equation is derived which gives the rate of change of f(N) with volume.
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