The Poisson distribution on a fractal

Details The Poisson distribution on a fractal The Poisson distribution on a fractal

Jul 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994a%26a...287..361d&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 287, no. 2, p. 361-367

Mathematics

Probability

Cosmology, Fractals, Mass Distribution, Poisson Density Functions, Statistical Analysis, Universe, Correlation, Dust, Probability Theory, Sampling

Scientific paper

Although the galaxy distribution is observed to be scale invariant at some scale, it cannot be identified to a perfect fractal which is a mathematical idealization. In this letter we illustrate, by a simple example, the fact that discretisation and finite sampling effects modify the expected properties of a fractal-like distribution: sampling an ideal fractal by a finite sequence of independent observations, we obtain a Poisson distribution on a fractal. Analyzing its main properties, with emphasis on number counts probabilites and mean N-points correlation functions, we illustrate these effects. Although this is not intended to modelize the galaxy distribution, we point out some similarities which justify the interest of this distribution for tests on statistical methods.

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