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Да смотрел я на эту страницу.. Там идет обоснование того почему Goodness-of-fit statistics делиться на два других подвида. MINITAB provides two goodness-of-fit statistics—Anderson-Darling for the maximum
likelihood and least squares estimation methods and Pearson correlation coefficient for
the least squares estimation method—to help you compare the fit of competing
distributions.
The Anderson-Darling statistic is a measure of how far the plot points fall from the fitted
line in a probability plot. The statistic is a weighted squared distance from the plot
points to the fitted line with larger weights in the tails of the distribution. Minitab uses
an adjusted Anderson-Darling statistic, because the statistic changes when a different
plot point method is used. A smaller Anderson-Darling statistic indicates that the
distribution fits the data better.
For least squares estimation, Minitab calculates a Pearson correlation coefficient. If the
distribution fits the data well, then the plot points on a probability plot will fall on a
straight line. The correlation measures the strength of the linear relationship between
the X and Y variables on a probability plot. The correlation will range between 0 and 1,
and higher values indicate a better fitting distribution.
Use the Anderson-Darling statistic and Pearson correlation coefficient to compare the fit
of different distributions.
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