On the use of C-stat in testing models for X-ray spectra

Abstract

Context. It has been shown that for the analysis of X-ray spectra the C-statistic, contrary to the χ²-statistic, provides unbiased estimates of the model parameters and their uncertainty ranges.
Aims: However, it is often stated that the C-statistic cannot be used to carry out statistical tests on the goodness of fit of the model, and therefore several investigations are still based on χ²-statistics.
Methods: Here we show that it is straightforward to calculate the expected value and variance of the C-statistic so that it can be used in tests.
Results: We provide formulae and simple numerical approximations to evaluate these expected values and variances. We also give examples indicating that tests based on only the expected value and variance of the C-statistic are reliable for spectra even with only 30 counts.
Conclusions: The C-statistic can be used for statistical tests such as assessing the goodness of fit of a spectral model.