Come analyze HEASARC, IRSA, and MAST data in the cloud! The Fornax Initiative is now welcoming all interested beta users.
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 |lstat |pgstat |pstat |whittle[#] |chistokes |chicov] [<weight method>] [<spectrum range>] | ||
|---|---|---|---|---|
| statistic test | [ad |chi |cusum |cvm |ks |pchi |runs] [<weight method>] [<spectrum range>] |
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 whittle with a number appended (e.g. whittle5) then the statistic is appropriate for that number of power density functions averaged together.
Earlier versions accepted cstat with a number appended (e.g. cstat5, optionally followed by b), which binned the data to a minimum number of counts per channel while calculating the statistic. This option has been removed: it never applied the documented threshold (the test was made against counts multiplied by the exposure, so the effective threshold was the appended number divided by the exposure time, making cstat1 through cstat20 behave identically for a typical observation), and its analytic derivatives and degrees of freedom did not account for the binning. Group the data before fitting instead — with the group command, which also recompresses the response, or with an external tool such as ftgrouppha — and then use plain cstat.
The chistokes statistic (with the general alias chicov) is a multivariate-Gaussian generalization of chi-squared for spectra that are correlated bin-by-bin, such as the Stokes I, Q and U spectra of a polarized source. It uses a per-bin covariance between the spectra (carried in the data files) rather than treating them as independent. The statistic acts on the covariance-group members currently assigned chistokes or chicov (the active sub-block); the given spectrum range must cover every active member of a group, all of which must share an identical grouping and be noticed identically. See Appendix B for the full description, the non-positive-definite (shrinkage) handling and the file format.
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.
XSPEC>statistic cstat 2-3 // Spectrum 1 continues to use chi-sq, 2 and 3 use cstat. XSPEC>data 4 spec4.pha // New spectrum 4 will use chi-sq. XSPEC>statistic cstat // All 4 spectra now use cstat, cstat is the new default. XSPEC>data 5 spec5.pha // New spectrum 5 will use cstat. XSPEC>statistic test ks // All 5 spectra now use ks as the test statistic. XSPEC>statistic chi churazov 5 // Spectrum 5 will use chi-sq using the churazov weighting