The table below provides an overview of the Goodness of Fit (GoF) tests available in the Statistical Toolkit; please refer to the User Documentation and the associated publications for further details.
GoF test | Type of distribution | Class | Notes on applicability |
Anderson-Darling | Binned Unbinned |
AndersonDarlingBinnedComparisonAlgorithm AndersonDarlingUnbinnedComparisonAlgorithm |
The mathematical formulation of the test statistics makes it is sensitive to the tails of the distributions. It can be applied also in case of fat tails. |
Anderson-Darling approximated | Binned Unbinned |
AndersonDarlingBinnedApproximatedComparisonAlgorithm AndersonDarlingUnbinnedApproximatedComparisonAlgorithm |
The mathematical formulation of the test statistics makes it is sensitive to the tails of the distributions. It can be applied also in case of fat tails. |
Chi-squared | Binned | Chi2ComparisonAlgorithm | It cannot applied if the counting per bin is lower than 5. |
Chi-squared (Incomplete Gamma function) |
Binned | Chi2ApproximatedComparisonAlgorithm | It cannot applied if the counting per bin is lower than 5. |
Chi-squared (Gamma function) |
Binned | Chi2IntegratingComparisonAlgorithm | It cannot applied if the counting per bin is lower than 5. |
Fisz-Cramer-von Mises | Binned Unbinned |
CramerVonMisesBinnedComparisonAlgorithm CramerVonMisesUnbinnedComparisonAlgorithm |
This test is satisfactory in case of symmetric or right-skewed distributions. |
Girone | Unbinned | GironeComparisonAlgorithm | This test is a modified version of Cramer-von Mises statistics. This test can be applied only if the two samples have the same size. |
Goodman | Unbinned | KolmogorovSmirnovApproximatedComparisonAlgorithm | It is the approximation of Kolmogorov-Smirnov test to a chi-squared statistics. Since it is based on the assumptions of Kolmogorov theorem, it may be applied to unbinned data. |
Kolmogorov-Smirnov | Unbinned | KolmogorovSmirnovComparisonAlgorithm | It derives from Kolmogorov statistics; since it is based on the Kolmogorov theorem, it may be applied to unbinned data. |
Kuiper | Unbinned | KuiperComparisonAlgorithm | It can be applied on cyclic observations, because the test statistics is invariant with
respect to the choice of the origin. It is sensitive both to the tails and to the median of the distributions. |
Tiku | Binned Unbinned |
TikuBinnedComparisonAlgorithm TikuUnbinnedComparisonAlgorithm |
This algorithm converts the Cramer-von Mises test statistics into a chi-squared. |
Watson | Unbinned | WatsonComparisonAlgorithm | It can be applied on cyclic observations, because the test statistics is invariant with respect to the choice of the origin. |
Weighted Cramer von Mises (Buning weighting function) |
Unbinned | WeightedCramerVonMisesBuningUnbinnedComparisonAlgorithm | This test is a modified version of Cramer-von Mises test. The mathematical formulation of the test statistics emphasises the lower part of the underlying distributions. |
Weighted Kolmogorov-Smirnov (AD weighting function) |
Unbinned | WeightedADKolmogorovSmirnovComparisonAlgorithm | This test is a modified version of Kolmogorov-Smirnov test. The mathematical formulation of the test statistics makes it is sensitive to the tails of the distributions. It can be applied also in case of fat tails. |
Weighted Kolmogorov-Smirnov (Buning weighting function) |
Unbinned | WeightedBuningKolmogorovSmirnovComparisonAlgorithm | This test is a modified version of Kolmogorov-Smirnov test. The mathematical formulation of the test statistics emphasises the lower part of the underlying distributions. |
More detailed statistical documentation can be retrieved in:
Introduction to
Goodness of Fit tests
GoF
algorithms
Applicability
of GoF tests
Power
of GoF Tests
and in the publications associated to the Statistical Toolkit.
Last modified 10 April 2006 - Maria Grazia Pia