public void FrechetDistributionTest2()
{
var frechet = new FrechetDistribution(-1, 2, 3);
AssertEqual("Location", -1, frechet.Location);
AssertEqual("Scale", 2, frechet.Scale);
AssertEqual("Shape", 3, frechet.Shape);
AssertEqual("Mean", 1.7082358814691916, frechet.Mean);
AssertEqual("Median", 1.2598945526747802, frechet.Median);
AssertEqual("Variance", 3.3812125776279194, frechet.Variance);
var x = new[] { 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 };
var expectedPdf = new[]
{
0.0402073567615389, 0.112944127838169, 0.2203072066895, 0.338481103916981, 0.443003781677631, 0.519397555251499,
0.56394859909252, 0.579937498912823, 0.573663383639088
};
var expectedCdf = new[]
{
0.00245281629310705, 0.00975837264521781, 0.0262174755427451, 0.0541795420336448, 0.0934461101976254, 0.141830159087343,
0.196256462270027, 0.253664662024469, 0.311501607580123
};
var expectedQuantile = new[]
{
0.514577262661815, 0.706626899067589, 0.87999965676962, 1.05913852685906, 1.25989455267478, 1.50191434769605,
1.82015164486637, 2.29737657865596, 3.23451848624939
};
Check(frechet, x, expectedPdf, expectedCdf, expectedQuantile);
}
public void FrechetDistributionTest1()
{
var frechet = new FrechetDistribution();
AssertEqual("Location", 0, frechet.Location);
AssertEqual("Scale", 1, frechet.Scale);
AssertEqual("Mean", double.PositiveInfinity, frechet.Mean);
AssertEqual("Median", 1.4426950408889634, frechet.Median);
AssertEqual("Variance", double.PositiveInfinity, frechet.Variance);
var x = new[] { 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 };
var expectedPdf = new[]
{
0.00453999297624848, 0.168448674977137, 0.39637770385836, 0.513031241399367, 0.541341132946451, 0.524654452326561,
0.489083747840359, 0.447663745094047, 0.406411096059143
};
var expectedCdf = new[]
{
4.53999297624849e-05, 0.00673794699908547, 0.0356739933472524, 0.0820849986238988, 0.135335283236613, 0.188875602837562,
0.239651036441776, 0.28650479686019, 0.329192987807906
};
var expectedQuantile = new[]
{
0.434294481903252, 0.621334934559612, 0.830583545082537, 1.09135666793729, 1.44269504088896, 1.95761518897122,
2.80367325205713, 4.48142011772455, 9.4912215810299
};
Check(frechet, x, expectedPdf, expectedCdf, expectedQuantile);
}
public void BivariateAssociationDiscreteNullDistribution()
{
Random rng = new Random(1);
// Pick very non-normal distributions for our non-parameteric tests
ContinuousDistribution xd = new FrechetDistribution(1.0);
ContinuousDistribution yd = new CauchyDistribution();
// Pick small sample sizes to get exact distributions
foreach (int n in TestUtilities.GenerateIntegerValues(4, 24, 4))
{
// Do a bunch of test runs, recording reported statistic for each.
List <int> spearmanStatistics = new List <int>();
List <int> kendallStatistics = new List <int>();
DiscreteDistribution spearmanDistribution = null;
DiscreteDistribution kendallDistribution = null;
for (int i = 0; i < 512; i++)
{
List <double> x = new List <double>();
List <double> y = new List <double>();
for (int j = 0; j < n; j++)
{
x.Add(xd.GetRandomValue(rng));
y.Add(yd.GetRandomValue(rng));
}
DiscreteTestStatistic spearman = Bivariate.SpearmanRhoTest(x, y).UnderlyingStatistic;
if (spearman != null)
{
spearmanStatistics.Add(spearman.Value);
spearmanDistribution = spearman.Distribution;
}
DiscreteTestStatistic kendall = Bivariate.KendallTauTest(x, y).UnderlyingStatistic;
if (kendall != null)
{
kendallStatistics.Add(kendall.Value);
kendallDistribution = kendall.Distribution;
}
}
// Test whether statistics are actually distributed as claimed
if (spearmanDistribution != null)
{
TestResult spearmanChiSquared = spearmanStatistics.ChiSquaredTest(spearmanDistribution);
Assert.IsTrue(spearmanChiSquared.Probability > 0.01);
}
if (kendallDistribution != null)
{
TestResult kendallChiSquared = kendallStatistics.ChiSquaredTest(kendallDistribution);
Assert.IsTrue(kendallChiSquared.Probability > 0.01);
}
}
}
