public void KendallNullDistributionTest()
{
// pick independent distributions for x and y, which needn't be normal and needn't be related
Distribution xDistrubtion = new LogisticDistribution();
Distribution yDistribution = new ExponentialDistribution();
Random rng = new Random(314159265);
// generate bivariate samples of various sizes
//int n = 64; {
foreach (int n in TestUtilities.GenerateIntegerValues(4, 64, 8)) {
Sample testStatistics = new Sample();
Distribution testDistribution = null;
for (int i = 0; i < 128; i++) {
BivariateSample sample = new BivariateSample();
for (int j = 0; j < n; j++) {
sample.Add(xDistrubtion.GetRandomValue(rng), yDistribution.GetRandomValue(rng));
}
TestResult result = sample.KendallTauTest();
testStatistics.Add(result.Statistic);
testDistribution = result.Distribution;
}
//TestResult r2 = testStatistics.KolmogorovSmirnovTest(testDistribution);
//Console.WriteLine("n={0} P={1}", n, r2.LeftProbability);
//Assert.IsTrue(r2.RightProbability > 0.05);
Console.WriteLine("{0} {1}", testStatistics.PopulationVariance, testDistribution.Variance);
Assert.IsTrue(testStatistics.PopulationMean.ConfidenceInterval(0.95).ClosedContains(testDistribution.Mean));
Assert.IsTrue(testStatistics.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(testDistribution.Variance));
}
}
public void GammaFromExponential()
{
// test that x_1 + x_2 + ... + x_n ~ Gamma(n) when z ~ Exponential()
Random rng = new Random(1);
ExponentialDistribution eDistribution = new ExponentialDistribution();
// pick some low values of n so distribution is not simply normal
foreach (int n in new int[] { 2, 3, 4, 5 }) {
Sample gSample = new Sample();
for (int i = 0; i < 100; i++) {
double sum = 0.0;
for (int j = 0; j < n; j++) {
sum += eDistribution.GetRandomValue(rng);
}
gSample.Add(sum);
}
GammaDistribution gDistribution = new GammaDistribution(n);
TestResult result = gSample.KolmogorovSmirnovTest(gDistribution);
Assert.IsTrue(result.LeftProbability < 0.95);
}
}
public void SignTestDistribution()
{
// start with a non-normally distributed population
Distribution xDistribution = new ExponentialDistribution();
Random rng = new Random(1);
// draw 100 samples from it and compute the t statistic for each
Sample wSample = new Sample();
for (int i = 0; i < 100; i++) {
// each sample has 8 observations
Sample xSample = new Sample();
for (int j = 0; j < 8; j++) { xSample.Add(xDistribution.GetRandomValue(rng)); }
//Sample xSample = CreateSample(xDistribution, 8, i);
TestResult wResult = xSample.SignTest(xDistribution.Median);
double W = wResult.Statistic;
//Console.WriteLine("W = {0}", W);
wSample.Add(W);
}
// sanity check our sample of t's
Assert.IsTrue(wSample.Count == 100);
// check that the t statistics are distributed as expected
DiscreteDistribution wDistribution = new BinomialDistribution(0.5, 8);
// check on the mean
Console.WriteLine("m = {0} vs. {1}", wSample.PopulationMean, wDistribution.Mean);
Assert.IsTrue(wSample.PopulationMean.ConfidenceInterval(0.95).ClosedContains(wDistribution.Mean));
// check on the standard deviation
Console.WriteLine("s = {0} vs. {1}", wSample.PopulationStandardDeviation, wDistribution.StandardDeviation);
Assert.IsTrue(wSample.PopulationStandardDeviation.ConfidenceInterval(0.95).ClosedContains(wDistribution.StandardDeviation));
// check on the skew
Console.WriteLine("t = {0} vs. {1}", wSample.PopulationMomentAboutMean(3), wDistribution.MomentAboutMean(3));
Assert.IsTrue(wSample.PopulationMomentAboutMean(3).ConfidenceInterval(0.95).ClosedContains(wDistribution.MomentAboutMean(3)));
// check on the kuritosis
Console.WriteLine("u = {0} vs. {1}", wSample.PopulationMomentAboutMean(4), wDistribution.MomentAboutMean(4));
Assert.IsTrue(wSample.PopulationMomentAboutMean(4).ConfidenceInterval(0.95).ClosedContains(wDistribution.MomentAboutMean(4)));
// KS tests are only for continuous distributions
}
public void MultivariateMoments()
{
// create a random sample
MultivariateSample M = new MultivariateSample(3);
Distribution d0 = new NormalDistribution();
Distribution d1 = new ExponentialDistribution();
Distribution d2 = new UniformDistribution();
Random rng = new Random(1);
int n = 10;
for (int i = 0; i < n; i++) {
M.Add(d0.GetRandomValue(rng), d1.GetRandomValue(rng), d2.GetRandomValue(rng));
}
// test that moments agree
for (int i = 0; i < 3; i++) {
int[] p = new int[3];
p[i] = 1;
Assert.IsTrue(TestUtilities.IsNearlyEqual(M.Column(i).Mean, M.Moment(p)));
p[i] = 2;
Assert.IsTrue(TestUtilities.IsNearlyEqual(M.Column(i).Variance, M.MomentAboutMean(p)));
for (int j = 0; j < i; j++) {
int[] q = new int[3];
q[i] = 1;
q[j] = 1;
Assert.IsTrue(TestUtilities.IsNearlyEqual(M.TwoColumns(i, j).Covariance, M.MomentAboutMean(q)));
}
}
}
