function AndersonDarling(const Data: TVec; Distribution: TDistribution; out hRes: THypothesisResult; out Signif: Double; Alpha: Double): Double;
Anderson-Darling GOF test.
| # | Name | Description |
|---|---|---|
| 1 | Data | Stores ordered data. |
| 2 | Distribution | Perform test for this distribution. Supported distributions : exponential, log-normal, normal and weibull. |
| 3 | hRes | Returns the result of the null hypothesis. |
| 4 | Signif | (Significance level) returns the probability of observing the given result by chance given that the null hypothesis is true. |
| 5 | Alpha | Defines the desired significance level. If the significance probability (Signif) is bellow the desired significance (Alpha), the null hypothesis is rejected. |
Returns: Double - Anderson-Darling test statistics, adjusted with small sample size factor.
The Anderson-Darling test (Stephens, 1974) is used to test if a sample of data came from a population with a specific distribution. It is a modification of the Kolmogorov-Smirnov (K-S) test and gives more weight to the tails than does the K-S test. The K-S test is distribution free in the sense that the critical values do not depend on the specific distribution being tested. The Anderson-Darling test makes use of the specific distribution in calculating critical values. This has the advantage of allowing a more sensitive test and the disadvantage that critical values must be calculated for each distribution.
The Anderson-Darling test is defined as:
- H0: The data follow a specified distribution.
- Ha: The data do not follow the specified distribution.
The test statistics is defined as:
where F is the cumulative distribution function of distribution being tested.
To learn more about A-D test, check the following links:
- http://www.itl.nist.gov/div898/handbook/eda/section3/eda35e.htm
- http://Src.alionscience.com/pdf/A_DTest.pdf
Note
The basic assumption is that the data values are sorted in ascending order.