Chi2ModVar

class sherpa.stats.Chi2ModVar(name: str = 'chi2modvar')[source] [edit on github]

Bases: 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.

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: Data | DataSimulFit, model: Model) → ndarray [edit on github]

Return the chi-square value for each bin.

Parameters:

data (sherpa.data.Data or sherpa.data.DataSimulFit) – The data set, or sets, to use.
model (sherpa.models.model.Model or sherpa.models.model.SimulFitModel) – The model expression, or expressions. If a sherpa.models.model.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: Data | DataSimulFit, model: Model) → tuple[float, ndarray] [edit on github]

Return the statistic value for the data and model.

Parameters:

data (sherpa.data.Data or sherpa.data.DataSimulFit) – The data set, or sets, to use.
model (sherpa.models.model.Model or sherpa.models.model.SimulFitModel) – The model expression, or expressions. If a sherpa.models.model.SimulFitModel is given then it must match the number of data sets in the data parameter.

Returns:

statval (number) – The value of the statistic.
fvec (array of numbers) – The per-bin “statistic” value.

static calc_staterror(data: ndarray) → ndarray[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: float, dof: int) → tuple[Literal[None], Literal[None]] | tuple[float, float] [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 (float or NaN or None) – The reduced statistic. If the statistic does not support a goodness of fit then the return value is 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.
qval (float or NaN or None) – The 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.