Astron. Astrophys. Suppl. Ser. 132, 301-304

A statistical method for testing assumed distributions of sources

Yi-Ping Qin¹ - G.Z. Xie¹ - Xue-Tang Zheng² - Shi-Min Wu³

1 - Yunnan Observatory, The Chinese Academy of Sciences, Kunming, Yunnan 650011, PR China
2 - Department of Physics, Nanjing University of Science and Technology, Nanjing, Jiangsu 210014, PR China
3 - Department of Astronomy, Beijing Normal University, Beijing 100875, PR China

Received November 14; accepted February 24, 1998

Abstract:

For a known distribution of sources, the variance of the distribution function of samples can be obtained by applying mathematical statistics. A statistical method, called the $1\sigma$distribution function deviation test, is defined and introduced to test this kind of distributions. We find that, when random variables vary continuously, a sample passing the test also passes any other statistical test which depends on the deviation of a statistic from its expected value at the $1\sigma$ confidence level. In particular, the sample passes the Kolmogorov-Smirnov test at the same confidence level. This new method is suitable for testing the distribution of gamma-ray bursts as well as the luminosity function of quasars.

An example of application of the new test is also presented in this paper.

Key words: galaxies: luminosity function, mass function -- galaxies: statistic -- methods: statistical