AAS 196th Meeting, June 2000
Session 54. Applications of Statistics
Special Contributed Display, Thursday, June 8, 2000, 9:20am-4:00pm, Empire Hall South

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[54.05] Goodness-of-fit Testing of Low-Count Data using the Modified Chi-Square-Gamma Statistic

K. Mighell (KPNO/NOAO)

I investigate the use of Pearson's chi-square statistic, the Maximum Likelihood Ratio statistic for Poisson distributions, and the chi-square-gamma statistic (Mighell 1999, ApJ, 518, 380) in the determination of the goodness-of-fit between theoretical models and low-count Poisson-distributed data. I demonstrate that these statistics should not be used to determine the goodness-of-fit with data values of 10 or less.

I modify the chi-square-gamma statistic for the purpose of improving its goodness-of-fit performance. I demonstrate that the modified chi-square-gamma statistic performs (nearly) like an ideal \chi2 statistic for the determination of goodness-of-fit with low-count data. On average, for the correct (true) models, the mean value of modified chi-square-gamma statistic is equal to the number of degrees of freedom (\nu) and its variance is 2\nu like the \chi2 distribution for \nu degrees of freedom. Probabilities for modified chi-square-gamma goodness-of-fit determinations can be made using the incomplete gamma function.

Simulated X-ray observations of a background flux of 0.06 photons per pixel and a point source of 40 photons spread over 317 pixels are analyzed as a practical demonstration of the use of the modified chi-square-gamma statistic in experimental astrophysics.

This research is supported by a grant from the National Aeronautics and Space Administration (NASA), Order No.\ S-67046-F, which was awarded by the Long-Term Space Astrophysics Program (NRA 95-OSS-16).

If you would like more information about this abstract, please follow the link to http://www.noao.edu/staff/mighell/aas196/. This link was provided by the author. When you follow it, you will leave the Web site for this meeting; to return, you should use the Back comand on your browser.

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