A statistical method for testing assumed distributions of sources

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: 14 November 1998
Accepted: 24 February 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 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 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.