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

¹ SRON Netherlands Institute for Space Research, Sorbonnelaan 2, 3584 CA Utrecht, The Netherlands
e-mail: J.S.Kaastra@sron.nl
² Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
³ Department of Physics and Astronomy, Universiteit Utrecht, PO Box 80000, 3508 TA Utrecht, The Netherlands

Received: 15 July 2016
Accepted: 22 July 2017

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.