Parameter Estimation with Few Counts using the chi (2_gamma ) Statistic

Details Parameter Estimation with Few Counts using the chi (2_gamma ) Statistic Parameter Estimation with Few Counts using the chi (2_gamma ) Statistic

Sep 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998aas...192.8104m&link_type=abstract

American Astronomical Society, 192nd AAS Meeting, #81.04; Bulletin of the American Astronomical Society, Vol. 30, p.1154

Statistics

Scientific paper

We propose a new chi (2) statistic, chi (2_gamma ) , which we suggest should always be used to analyze Poisson-distributed data in preference to the modified Neyman's chi (2) statistic. We demonstrate the power and usefulness of chi (2_gamma ) minimization by using two statistical fitting techniques and five statistics to analyze simulated X-ray power-law 15-channel spectra with large and small counts per bin. We show that chi (2_gamma ) minimization with the Levenberg-Marquardt or Powell's method can produce excellent results (mean slope errors <~ 3%) with spectra having as few as 25 total counts.

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