AndersonDarlingTest Class

public sealed class AndersonDarlingTest : OneSampleTest

Public NotInheritable Class AndersonDarlingTest
	Inherits OneSampleTest

public ref class AndersonDarlingTest sealed : public OneSampleTest

[<SealedAttribute>]
type AndersonDarlingTest = 
    class
        inherit OneSampleTest
    end

Inheritance

Object  →  HypothesisTest  →  OneSampleTest<Double>  →  OneSampleTest  →  AndersonDarlingTest

The Anderson-Darling test is a statistical test used to determine if a sample of data comes from a specific distribution, in this case, the normal distribution. The null hypothesis for this test is that the sample is drawn from a population that follows the specified distribution.

The test statistic is calculated based on the cumulative distribution function (CDF) of the specified distribution. The Anderson-Darling test gives more weight to the tails of the distribution than the Kolmogorov-Smirnov test, making it more sensitive to deviations in the tails.

The distribution of the test statistic under the null hypothesis is used to determine the p-value, which indicates the probability of observing the test statistic as extreme as, or more extreme than, the value calculated from the sample data, assuming the null hypothesis is true.

Applications of the Anderson-Darling test include testing for normality in quality control, finance, and other fields where the assumption of normality is critical. The test can also be applied to other distributions by specifying the appropriate distribution type.

The AndersonDarlingDistribution class implements the distribution of the Anderson-Darling test statistic for various distributions.

Use the AndersonDarlingTest class to test whether a sample comes from a normal distribution. The Anderson-Darling test is a variation of the Kolmogorov-Smirnov test that gives more weight to the tails of the distribution. In addition, the parameters of the distribution may be estimated from the sample. This makes the test more applicable in a larger number of cases.

The Mean and StandardDeviation of the distribution may be specified, but this is not necessary.

The following example demonstrates how to use the Anderson-Darling test with different constructors and how to access its properties and methods.

using Numerics.NET.Statistics;
using Numerics.NET.Statistics.Tests;
using Numerics.NET.Statistics.Distributions;

// Example 1: Using the default constructor
Vector<double> data1 = [ 1.0, 2.0, 3.0, 4.0, 5.0 ];
var test1 = new AndersonDarlingTest(data1);
double statistic1 = test1.CalculateStatistic();
double pValue1 = test1.GetPValue(HypothesisType.OneTailedUpper);
Console.WriteLine($"Statistic: {statistic1}, P-Value: {pValue1}");

// Example 2: Using the constructor with a specified distribution
Vector<double> data2 = [ 1.0, 2.0, 3.0, 4.0, 5.0 ];
var normalDist = new NormalDistribution(0, 1);
var test2 = new AndersonDarlingTest(data2, normalDist);
double statistic2 = test2.CalculateStatistic();
double pValue2 = test2.GetPValue(HypothesisType.OneTailedUpper);
Console.WriteLine($"Statistic: {statistic2}, P-Value: {pValue2}");

// Example 3: Using the constructor with a specified CDF function
Vector<double> data3 = [ 1.0, 2.0, 3.0, 4.0, 5.0 ];
Func<double, double> cdf = x => new NormalDistribution(0, 1).DistributionFunction(x);
var test3 = new AndersonDarlingTest(data3, cdf);
double statistic3 = test3.CalculateStatistic();
double pValue3 = test3.GetPValue(HypothesisType.OneTailedUpper);
Console.WriteLine($"Statistic: {statistic3}, P-Value: {pValue3}");

// Example 4: Using the constructor with specified mean and standard deviation
Vector<double> data4 = [ 1.0, 2.0, 3.0, 4.0, 5.0 ];
var test4 = new AndersonDarlingTest(data4, 2, 3);
double statistic4 = test4.CalculateStatistic();
double pValue4 = test4.GetPValue(HypothesisType.OneTailedUpper);
Console.WriteLine($"Statistic: {statistic4}, P-Value: {pValue4}");

Reference