Statistics
Scientific paper
Jan 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987baas...19r.651m&link_type=abstract
Bulletin of the American Astronomical Society, Vol. 19, p.651-651
Statistics
Scientific paper
To study the bright-end of galaxian luminoosity functions in clusters of galaxies, Tremaine & Richstone (1977) devised two statistics T1 = s(M1)/mean(M2-M1) and T2 = (0.677)-1/2 s(M2-M1)/ mean(M2-M1), and state that for samples of large clusters, T1 >= 1 and T2 >= 1, if the galaxy luminosities are randomly drawn fro a given parent luminosity function (which may vary from cluster to cluster). A galaxy system in which significant evolution (such as mergers) would be taking place would show T1 < 1. The distribution of these two statistics is studied here for different cluster (or group) sizes (membership), different sample sizes, and also different selection effects. The distributions of T1 and T2 are generally centered near unity with a 1 sigma dispersion ~ 0.15. The mean and median values of T1 and T2 decrease with smaller cluster size, while their dispersion increases with smaller sample sizes. Selection effects can alter appreciably the distribution of these two statistics. In summary, one should not blindly compare T1 or T2 to unity, but instead consider their values relative to the sizes of the clusters or groups, the sample size, and the selection effects incorporated in the sample.
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