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Astron. Astrophys. 341, 693-696 (1999)

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A proposal for a sufficient test of luminosity functions

Yi-Ping Qin and G.-Z. Xie

Yunnan Observatory, Chinese Academy of Sciences, Kunming, Yunnan 650011, P.R. China

Received 7 July 1998 / Accepted 9 October 1998


A new statistic [FORMULA] is introduced in this paper. If the proposed luminosity function correctly describes the distribution of the adopted sample, then the values of [FORMULA] would be uniformly distributed in the interval [FORMULA]. We find that the [FORMULA] test of the luminosity function is a necessary one, and the [FORMULA] test is independent of the [FORMULA] test which is a revision of the famous [FORMULA] test, presented in our previous work (Qin & Xie 1997). It is proved that two given distributions of [FORMULA] and [FORMULA] correspond to a unique normalized luminosity function. The distributions of [FORMULA] and [FORMULA] 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

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© European Southern Observatory (ESO) 1999

Online publication: December 16, 1998