Maximum-Likelihood Statistics

The second method is to replace the $\chi^2$-minimization scheme with the Cash maximum-likelihood scheme (cstat in Xspec) when fitting data. This method is much better suited to data with low count rates and is a suitable option only if one is running Xspec v11.1.0 or later. The reason for this is that RGS spectrum files have prompted a slight modification to the OGIP standard. Because the RGS spatial extraction mask has a spatial-width which is a varying function of wavelength, it has become necessary to characterize the BACKSCL and AREASCL parameters as vectors (i.e., one number for each wavelength channel), rather than scalar keywords as they are for data from the EPIC cameras and past missions. These quantities map the size of the source extraction region to the size of the background extraction region and are essential for accurate fits.

One caveat of using the cstat option is that the scheme requires a ``total'' and ``background'' spectrum to be loaded into Xspec. This is in order to calculate parameter errors correctly.

To change schemes in Xspec before fitting the data in the Command Window, type:

xspec
statistic cstat