Chi2Gehrels¶
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class
sherpa.stats.
Chi2Gehrels
(name='chi2gehrels')[source] [edit on github]¶ Bases:
sherpa.stats.Chi2
Chi Squared with Gehrels variance.
The variance is estimated from the number of counts in each bin, but unlike Chi2DataVar, the Gaussian approximation is not used. This makes it more-suitable for use with low-count data.
The standard deviation for each bin is calculated using the approximation from [1]:
sigma(i,S) = 1 + sqrt(N(i,s) + 0.75)where the higher-order terms have been dropped. This is accurate to approximately one percent. For data where the background has not been subtracted then the error term is:
sigma(i) = sigma(i,S)whereas with background subtraction,
sigma(i)^2 = sigma(i,S)^2 + [A(S)/A(B)]^2 sigma(i,B)^2See also
Notes
The accuracy of the error term when the background has been subtracted has not been determined. A preferable approach to background subtraction is to model the background as well as the source signal.
References
[1] “Confidence limits for small numbers of events in astrophysical data”, Gehrels, N. 1986, ApJ, vol 303, p. 336-346. http://adsabs.harvard.edu/abs/1986ApJ…303..336G 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
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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
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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
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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
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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
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