Chi2ModVar¶
- class sherpa.stats.Chi2ModVar(name='chi2modvar')[source] [edit on github]¶
Bases:
sherpa.stats.Chi2
Chi Squared with model amplitude variance.
The variance in each bin is estimated from the model value in that bin. This contrasts with other Chi-squared statics - such as Chi2DataVar, Chi2XspecVar`, and Chi2Gehrels - which use the data values. The variance is
sigma(i)^2 = S(i) + [A(S)/A(B)]^2 B(i,off)
where B(i,off) is the background model amplitude in bin i of the off-source region.
A(B) is the off-source “area”, which could be the size of the region from which the background is extracted, or the length of a background time segment, or a product of the two, etc.; and A(S) is the on-source “area”. These terms may be defined for a particular type of data: for example, PHA data sets A(B) to BACKSCAL * EXPOSURE from the background data set and A(S) to BACKSCAL * EXPOSURE from the source data set.
See also
Notes
The background should not be subtracted from the data when this statistic is used, as it underestimates the variance when fitting background-subtracted data.
Methods Summary
calc_chisqr
(data, model)Return the chi-square value for each bin.
calc_stat
(data, model)Return the statistic value for the data and model.
calc_staterror
(data)Return the statistic error values for the data.
goodness_of_fit
(statval, dof)Return the reduced statistic and q value.
Methods Documentation
- calc_chisqr(data, model) [edit on github]¶
Return the chi-square value for each bin.
- Parameters
data (a Data or DataSimulFit instance) – The data set, or sets, to use.
model (a Model or SimulFitModel instance) – The model expression, or expressions. If a SimulFitModel is given then it must match the number of data sets in the data parameter.
- Returns
chisqr – The per-bin chi-square values.
- Return type
array of numbers
- calc_stat(data, model) [edit on github]¶
Return the statistic value for the data and model.
- Parameters
data (a Data or DataSimulFit instance) – The data set, or sets, to use.
model (a Model or SimulFitModel instance) – The model expression, or expressions. If a SimulFitModel is given then it must match the number of data sets in the data parameter.
- Returns
statval, fvec – The statistic value and the per-bin “statistic” value.
- Return type
number, array of numbers
- static calc_staterror(data)[source] [edit on github]¶
Return the statistic error values for the data.
- Parameters
data (scalar or 1D array of numbers) – The data values.
- Returns
staterror – The errors for the input data values (matches the data argument).
- Return type
scalar or array of numbers
- goodness_of_fit(statval, dof) [edit on github]¶
Return the reduced statistic and q value.
The reduced statisitc is conceptually simple, as it is just statistic / degrees-of-freedom, but it is not meaningful for all statistics, and it is only valid if there are any degrees of freedom.
- Parameters
statval (float) – The statistic value. It is assumed to be finite.
dof (int) – The number of degrees of freedom, which may be 0 or negative.
- Returns
rstat, qval – The reduced statistic and q value. If the statistic does not support a goodness of fit then the return values are None. If it does then NaN is returned if either the number of degrees of freedom is 0 (or less), or the statistic value is less than 0.
- Return type
float or NaN or None, float or NaN or None