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

## A statistical method for testing assumed distributions of sources

**Yi-Ping Qin**^{1} - G.Z. Xie^{1} - Xue-Tang Zheng^{2} -
Shi-Min Wu^{3}

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 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.

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

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