Chi2DataVar

class sherpa.stats.Chi2DataVar(name='chi2datavar')[source] [edit on github]

Bases: Chi2

Chi Squared with data variance.

The variance in each bin is estimated from the data value in that bin.

If the number of counts in each bin is large, then the shape of the Poisson distribution from which the counts are sampled tends asymptotically towards that of a Gaussian distribution, with variance

sigma(i)^2 = N(i,S) + [A(S)/A(B)]^2 N(i,B)

where N is the number of on-source (and off-source) bins included in the fit. The background term appears only if an estimate of the background has been subtracted from the data.

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.

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 (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, model) [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)[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 (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.