public void TestMethod1()
{
Distribution n0 = new TransformedDistribution(new NormalDistribution(), -2.0, 3.0);
Distribution n1 = new NormalDistribution(-2.0, 3.0);
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.Mean, n1.Mean));
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.Variance, n1.Variance));
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.StandardDeviation, n1.StandardDeviation));
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.Skewness, n1.Skewness));
for (int k = 0; k < 8; k++)
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.Moment(k), n1.Moment(k)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.MomentAboutMean(k), n1.MomentAboutMean(k)));
}
foreach (double x in TestUtilities.GenerateUniformRealValues(-8.0, 8.0, 8))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.ProbabilityDensity(x), n1.ProbabilityDensity(x)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.LeftProbability(x), n1.LeftProbability(x)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.RightProbability(x), n1.RightProbability(x)));
}
foreach (double P in TestUtilities.GenerateRealValues(1.0E-4, 1.0, 4))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.InverseLeftProbability(P), n1.InverseLeftProbability(P)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.InverseRightProbability(P), n1.InverseRightProbability(P)));
}
}
/// <summary>
/// Tests whether the sample is compatible with the given distribution.
/// </summary>
/// <param name="sample">The sample.</param>
/// <param name="distribution">The distribution.</param>
/// <returns>The test result. The test statistic is the V statistic and the chance to obtain such a large
/// value of V under the assumption that the sample is drawn from the given distribution.</returns>
/// <remarks>
/// <para>Like the Kolmogorov-Smirnov test (<see cref="Univariate.KolmogorovSmirnovTest(IReadOnlyList{Double},ContinuousDistribution)"/>),
/// Kuiper's test compares the EDF of the sample to the CDF of the given distribution.</para>
/// <para>For small sample sizes, we compute the null distribution of V exactly. For large sample sizes, we use an accurate
/// asympototic approximation. Therefore it is safe to use this method for all sample sizes.</para>
/// </remarks>
/// <exception cref="ArgumentNullException"><paramref name="distribution"/> is <see langword="null"/>.</exception>
/// <exception cref="InsufficientDataException">There is no data in the sample.</exception>
/// <seealso href="http://en.wikipedia.org/wiki/Kuiper%27s_test"/>
public static TestResult KuiperTest(this IReadOnlyList <double> sample, ContinuousDistribution distribution)
{
if (sample == null)
{
throw new ArgumentNullException(nameof(sample));
}
if (distribution == null)
{
throw new ArgumentNullException(nameof(distribution));
}
int n = sample.Count;
if (n < 1)
{
throw new InsufficientDataException();
}
// Compute the V statistic, which is the sum of the D+ and D- statistics.
double DP, DM;
ComputeDStatistics(sample, distribution, out DP, out DM);
double V = DP + DM;
ContinuousDistribution VDistribution;
if (n < 32)
{
VDistribution = new TransformedDistribution(new KuiperExactDistribution(n), 0.0, 1.0 / n);
}
else
{
VDistribution = new TransformedDistribution(new KuiperAsymptoticDistribution(n), 0.0, 1.0 / Math.Sqrt(n));
}
return(new TestResult("V", V, TestType.RightTailed, VDistribution));
}
/// <summary>
/// Tests whether the sample is compatible with the given distribution.
/// </summary>
/// <param name="sample">The sample.</param>
/// <param name="distribution">The distribution.</param>
/// <returns>The test result. The test statistic is the D statistic and the probability is the chance of
/// obtaining such a large value of D under the assumption that the sample is drawn from the given distribution.</returns>
/// <remarks>
/// <para>The null hypothesis of the Kolmogorov-Smirnov (KS) test is that the sample is drawn from the given continuous distribution.
/// The test statsitic D is the maximum deviation of the sample's empirical distribution function (EDF) from
/// the distribution's cumulative distribution function (CDF). A high value of the test statistic, corresponding
/// to a low right tail probability, indicates that the sample distribution disagrees with the given distribution
/// to a degree unlikely to arise from statistical fluctuations.</para>
/// <para>For small sample sizes, we compute the null distribution of D exactly. For large sample sizes, we use an accurate
/// asympototic approximation. Therefore it is safe to use this method for all sample sizes.</para>
/// <para>A variant of this test, <see cref="Sample.KolmogorovSmirnovTest(Sample, Sample)"/>, allows you to non-parametrically
/// test whether two samples are drawn from the same underlying distribution, without having to specify that distribution.</para>
/// </remarks>
/// <exception cref="ArgumentNullException"><paramref name="distribution"/> is <see langword="null"/>.</exception>
/// <exception cref="InsufficientDataException">There is no data in the sample.</exception>
/// <seealso cref="KolmogorovDistribution"/>
/// <seealso href="http://en.wikipedia.org/wiki/Kolmogorov-Smirnov_test"/>
public static TestResult KolmogorovSmirnovTest(this IReadOnlyList <double> sample, ContinuousDistribution distribution)
{
if (sample == null)
{
throw new ArgumentNullException(nameof(sample));
}
if (distribution == null)
{
throw new ArgumentNullException(nameof(distribution));
}
int n = sample.Count;
if (n < 1)
{
throw new InsufficientDataException();
}
// Compute the D statistic, which is the maximum of the D+ and D- statistics.
double DP, DM;
ComputeDStatistics(sample, distribution, out DP, out DM);
double D = Math.Max(DP, DM);
ContinuousDistribution DDistribution;
if (n < 32)
{
DDistribution = new TransformedDistribution(new KolmogorovExactDistribution(n), 0.0, 1.0 / n);
}
else
{
DDistribution = new TransformedDistribution(new KolmogorovAsymptoticDistribution(n), 0.0, 1.0 / Math.Sqrt(n));
}
return(new TestResult("D", D, TestType.RightTailed, DDistribution));
}
