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A test (typically of distribution, independence, or goodness of fit), for the family of distributions use [chi-squared-distribution].
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chi-squared of simultaneous (least-squares) fitted data
One approach would be to calculate the six individual values, one for each data set, and then sum the relative contribution to the total based on the number of data points in each data set.
As an exa …
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Appropriate goodness of fit measure for signal with unknown errors
RMSE (Root Mean Squared Error) might be a good candidate, as historically it was used as a sort of "average magnitude of error". To calculate it, all errors are first squared (to remove any negative v …