Astronomy and Astrophysics – Astrophysics
Scientific paper
May 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000aas...196.5405m&link_type=abstract
American Astronomical Society, 196th AAS Meeting, #54.05; Bulletin of the American Astronomical Society, Vol. 32, p.762
Astronomy and Astrophysics
Astrophysics
Scientific paper
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 χ2 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 (ν ) and its variance is 2ν like the χ2 distribution for ν 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).
No associations
LandOfFree
Goodness-of-fit Testing of Low-Count Data using the Modified Chi-Square-Gamma Statistic does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Goodness-of-fit Testing of Low-Count Data using the Modified Chi-Square-Gamma Statistic, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Goodness-of-fit Testing of Low-Count Data using the Modified Chi-Square-Gamma Statistic will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1126185