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Introduction
There are two operations performed in XSPEC that require statistics. The first is parameter estimation, which comprises finding the parameters for a given model that provide the best fit to the data and then estimating uncertainties on these parameters. The second operation is testing whether the model and its best-fit parameters actually match the data. This is usually referred to as determining the goodness-of-fit.
Users can specify their statistic of choice with the statistic command. Which statistics should be used for these two operations depends on the probability distributions underlying the data. Almost all astronomical data are drawn from one of two distributions: Gaussian (or normal) and Poisson. The Poisson distribution is the familiar case of counting statistics and is valid whenever the only source of experimental noise is due to the number of events arriving at the detector. This is a good approximation for modern CCD instruments. If some other sort of noise is dominant then it is usually described by the Gaussian distribution. A common example of this is detectors that require background to be modeled in some way, rather than directly measured. The uncertainty in the background modeling is assumed to be Gaussian.
In the limit of large numbers of counts the Poisson distribution can be well approximated by a Gaussian so the latter is often used for detectors with high counting rates. In most cases this will cause no errors and does simplify the handling of background uncertainties however care should be exercised that no systematic offsets are introduced.
A fuller discussion of many of the issues discussed in this appendix can be found in Siemiginowska (2011).