Statistics::AndersonDarling Function

double AndersonDarling(TVec *Data, TDistribution Distribution, THypothesisResult &hRes, double &Signif, double Alpha = 0.05);

Anderson-Darling GOF test.

#NameTypeDescription
1DataTVec *Stores ordered data.
2DistributionTDistributionPerform test for this distribution. Supported distributions : exponential, log-normal, normal and weibull.
3hResTHypothesisResult &Returns the result of the null hypothesis.
4Signifdouble &(Significance level) returns the probability of observing the given result by chance given that the null hypothesis is true.
5Alpha = 0.05doubleDefines the desired significance level. If the significance probability (Signif) is bellow the desired significance (Alpha), the null hypothesis is rejected.

Returns: Anderson-Darling test statistics, adjusted with small sample size factor.

Remarks:

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:

A2=NS,whereS=i=1N2i1N[lnF(Yi)+ln(1F(YN+1i)]\begin{aligned} A^2 = -N -S \quad , \text{where} \\ S = \sum _{i=1} ^N \cfrac{2i-1}{N} \left[ \ln F(Y_i) + \ln \left(1-F(Y_{N+1-i} \right) \right] \end{aligned}

where F is the cumulative distribution function of distribution being tested.

To learn more about A-D test, check the following links:

Note

The basic assumption is that the data values are sorted in ascending order.

See Also: Statistics::GOFKolmogorov
Declared in Dew::Stats::Units::Statistics · Dew.Stats/Units.Statistics.h · Cross-compiler