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A proposal for a sufficient test of luminosity functions
Yi-Ping Qin and
Received 7 July 1998 / Accepted 9 October 1998
A new statistic is introduced in this paper. If the proposed luminosity function correctly describes the distribution of the adopted sample, then the values of would be uniformly distributed in the interval . We find that the test of the luminosity function is a necessary one, and the test is independent of the test which is a revision of the famous test, presented in our previous work (Qin & Xie 1997). It is proved that two given distributions of and correspond to a unique normalized luminosity function. The distributions of and therefore provide a sufficient test for any adopted forms of the luminosity function. As a demonstration, we present a simple application of the method to a luminosity function and a sample found in the literature.
Key words: methods: statistical galaxies: luminosity function galaxies: quasars: general cosmology: observations
Send offprint requests to: Yi-Ping Qin
Online publication: December 16, 1998