public void ConstructorTest()
{
var t = new TDistribution(degreesOfFreedom: 4.2);
double mean = t.Mean; // 0.0
double median = t.Median; // 0.0
double var = t.Variance; // 1.9090909090909089
double cdf = t.DistributionFunction(x: 1.4); // 0.88456136730659074
double pdf = t.ProbabilityDensityFunction(x: 1.4); // 0.13894002185341031
double lpdf = t.LogProbabilityDensityFunction(x: 1.4); // -1.9737129364307417
double ccdf = t.ComplementaryDistributionFunction(x: 1.4); // 0.11543863269340926
double icdf = t.InverseDistributionFunction(p: cdf); // 1.4000000000000012
double hf = t.HazardFunction(x: 1.4); // 1.2035833984833988
double chf = t.CumulativeHazardFunction(x: 1.4); // 2.1590162088918525
string str = t.ToString(CultureInfo.InvariantCulture); // T(x; df = 4.2)
Assert.AreEqual(0.0, mean);
Assert.AreEqual(0.0, median);
Assert.AreEqual(1.9090909090909089, var);
Assert.AreEqual(2.1590162088918525, chf);
Assert.AreEqual(0.88456136730659074, cdf);
Assert.AreEqual(0.13894002185341031, pdf);
Assert.AreEqual(-1.9737129364307417, lpdf);
Assert.AreEqual(1.2035833984833988, hf);
Assert.AreEqual(0.11543863269340926, ccdf);
Assert.AreEqual(1.4000000000000012, icdf);
Assert.AreEqual("T(x; df = 4.2)", str);
}
/// <summary>
/// Tests the null hypothesis that the population mean is equal to a specified value.
/// </summary>
///
public TTest(double[] sample, double hypothesizedMean, TTestHypotesis type)
{
int n = sample.Length;
double x = Accord.Statistics.Tools.Mean(sample);
double s = Accord.Statistics.Tools.StandardDeviation(sample, x);
StatisticDistribution = new TDistribution(n - 1);
Statistic = (x - hypothesizedMean) / (s / Math.Sqrt(n));
if (type == TTestHypotesis.MeanIsDifferentThanHypothesis)
{
PValue = 2.0 * StatisticDistribution.SurvivalFunction(Statistic);
Hypothesis = Testing.Hypothesis.TwoTail;
}
else if (type == TTestHypotesis.MeanIsGreaterThanHypothesis)
{
PValue = StatisticDistribution.SurvivalFunction(Statistic);
Hypothesis = Testing.Hypothesis.OneUpper;
}
else if (type == TTestHypotesis.MeanIsSmallerThanHypothesis)
{
PValue = StatisticDistribution.DistributionFunction(Statistic);
Hypothesis = Testing.Hypothesis.OneLower;
}
}
public void ConstructorTest()
{
var t = new TDistribution(degreesOfFreedom: 4.2);
double mean = t.Mean; // 0.0
double median = t.Median; // 0.0
double var = t.Variance; // 1.9090909090909089
double mode = t.Mode;
double cdf = t.DistributionFunction(x: 1.4); // 0.88456136730659074
double pdf = t.ProbabilityDensityFunction(x: 1.4); // 0.13894002185341031
double lpdf = t.LogProbabilityDensityFunction(x: 1.4); // -1.9737129364307417
double ccdf = t.ComplementaryDistributionFunction(x: 1.4); // 0.11543863269340926
double icdf = t.InverseDistributionFunction(p: cdf); // 1.4000000000000012
double hf = t.HazardFunction(x: 1.4); // 1.2035833984833988
double chf = t.CumulativeHazardFunction(x: 1.4); // 2.1590162088918525
string str = t.ToString(CultureInfo.InvariantCulture); // T(x; df = 4.2)
Assert.AreEqual(double.NegativeInfinity, t.Support.Min);
Assert.AreEqual(double.PositiveInfinity, t.Support.Max);
double icdf0 = t.InverseDistributionFunction(0);
double icdf1 = t.InverseDistributionFunction(1);
Assert.AreEqual(icdf0, t.Support.Min);
Assert.AreEqual(icdf1, t.Support.Max);
Assert.AreEqual(0.0, mean);
Assert.AreEqual(0.0, median);
Assert.AreEqual(0.0, mode);
Assert.AreEqual(1.9090909090909089, var);
Assert.AreEqual(2.1590162088918525, chf);
Assert.AreEqual(0.88456136730659074, cdf);
Assert.AreEqual(0.13894002185341031, pdf);
Assert.AreEqual(-1.9737129364307417, lpdf);
Assert.AreEqual(1.2035833984833988, hf);
Assert.AreEqual(0.11543863269340926, ccdf);
Assert.AreEqual(1.4000000000000012, icdf);
Assert.AreEqual("T(x; df = 4.2)", str);
var range1 = t.GetRange(0.95);
var range2 = t.GetRange(0.99);
var range3 = t.GetRange(0.01);
Assert.AreEqual(-2.1030107450099362, range1.Min);
Assert.AreEqual(2.1030107450099362, range1.Max);
Assert.AreEqual(-3.6502571302187774, range2.Min);
Assert.AreEqual(3.6502571302187774, range2.Max);
Assert.AreEqual(-3.6502571302187792, range3.Min);
Assert.AreEqual(3.6502571302187774, range3.Max);
}
public void DistributionFunctionTest()
{
TDistribution target = new TDistribution(1);
double expected = 0.5;
double actual = target.DistributionFunction(0);
Assert.IsFalse(Double.IsNaN(actual));
Assert.AreEqual(expected, actual, 1e-15);
expected = 0.92559723470138278;
actual = target.DistributionFunction(4.2);
Assert.AreEqual(expected, actual);
target = new TDistribution(2);
expected = 0.5;
actual = target.DistributionFunction(0);
Assert.AreEqual(expected, actual);
expected = 0.97385836652685043;
actual = target.DistributionFunction(4.2);
Assert.AreEqual(expected, actual);
target = new TDistribution(3);
expected = 0.5;
actual = target.DistributionFunction(0);
Assert.IsFalse(Double.IsNaN(actual));
Assert.AreEqual(expected, actual, 1e-15);
expected = 0.98768396091153043;
actual = target.DistributionFunction(4.2);
Assert.AreEqual(expected, actual);
expected = 0.16324737815131229;
actual = target.DistributionFunction(-1.17);
Assert.AreEqual(expected, actual);
}
protected override double InnerDistributionFunction(double x)
{
return(baseT.DistributionFunction((x - mean) / ScaleCoefficient));
}
protected override double InnerProbabilityDensityFunction(double x)
{
return(1d / (ub - ua) * (baseDistribution.DistributionFunction((x - tm - ua) / ts) - baseDistribution.DistributionFunction((x - tm - ub) / ts)));
}