## statistic

change the objective function (statistic) for the fit

Change the fit or test statistic in use, for one or more spectra.

 Syntax: statistic [chi |cstat[#[b]] | lstat |pgstat |pstat |whittle[#]] [] [] statistic test [ad |chi |cvm |ks | pchi |runs] [] []

The fit statistic options are chi-squared (chi), C statistic (cstat, note that this is the W statistic if there is background), Loredo statistic (lstat), a statistic for Poisson data with assumed known background (pstat), a statistic for Poisson data with Gaussian background (pgstat), and the Whittle statistic (whittle) for power density functions. If the statistic is given as cstat with a number appended (e.g. cstat5) then the statistic is calculated after the data are binned to contain a minimum number of counts in each channel where the minimum number is the number appended. If the number is followed by b then the binning is based on the minimum number of counts in the background spectrum. Note that this binning only occurs when calculating the statistic and has to be done every time so it is much less efficent than using an external program (such as ftgrouppha). If the statistic is given as whittle with a number appended (e.g. whittle5) then the statistic is appropriate for that number of power density functions averaged together.

The test statistic options are Anderson-Darling (ad), chi-squared (chi), Cramer-von Mises (cvm), CUSUM (cusum), Kolmogorov-Smirnov (ks), Pearson chi-square (pchi) and Runs (runs).

All These statistics are described in more in detail in Appendix B.

If a weight method is specified then that will be used if appropriate for the statistic. The weight options available are standard, gehrels, churazov, and model. standard weighting uses or the statistical error given in the input spectrum. gehrels weighting uses , a better approximation when N is small (Gehrels 1986). churazov weighting uses the suggestion of Churazov et al. (1996) to estimate the weight for a given channel by averaging the counts in surrounding channels. model weighting uses the value of the model, not the data, to estimate the weight.

If a spectrum number or spectrum range is given, the chosen statistic will only apply to those spectra. It is therefore possible for a multi-spectrum fit to use more than one fit or test statistic. If no spectrum number or range is given, the chosen statistic will apply to all loaded spectra and will be the default statistic for any future loaded spectra.

Examples:

Assume 3 spectra are currently loaded, all using the chi-squared statistic, and that chi-squared is the default statistic.

XSPEC12>statistic cstat 2-3
// Spectrum 1 continues to use chi-sq, 2 and 3 use cstat.
XSPEC12>statistic cstat5 3
// Spectrum 3 uses cstat but with a binning to a minimum
// number of 5 counts/bin.
XSPEC12>data 4 spec4.pha
// New spectrum 4 will use chi-sq.
XSPEC12>statistic cstat
// All 4 spectra now use cstat, cstat is the new default.
XSPEC12>data 5 spec5.pha
// New spectrum 5 will use cstat.
XSPEC12>statistic test ks
// All 5 spectra now use ks as the test statistic.
XSPEC12>statistic chi churazov 5
// Spectrum 5 will use chi-sq using the churazov weighting