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>
/// Gets the cumulative distribution function (cdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
/// <param name="x">A single point in the distribution range.</param>
/// <returns>System.Double.</returns>
/// <remarks>The Cumulative Distribution Function (CDF) describes the cumulative
/// probability that a given value or any value smaller than it will occur.</remarks>
protected internal override double InnerDistributionFunction(double x)
{
// http://graphpad.com/support/faqid/1598/
double N = NumberOfSamples;
double num = N * (N - 2) * x * x;
double den = ((N - 1) * (N - 1)) - N * x * x;
double t = Math.Sqrt(num / den);
double p = tDistribution.ComplementaryDistributionFunction(t);
double r = 1.0 - N * p;
if (r > 1)
{
return(1);
}
if (r < 0)
{
return(0);
}
return(r);
}
