public void TrapezoidalDistributionConstructorTest()
{
double x = 0.75d;
double a = 0;
double b = (1.0d / 3.0d);
double c = (2.0d / 3.0d);
double d = 1.0d;
double n1 = 2.0d;
double n3 = 2.0d;
var trapDist = new TrapezoidalDistribution(a, b, c, d, n1, n3);
double mean = trapDist.Mean; //0.62499999999999989
double variance = trapDist.Variance; //0.37103174603174593
double pdf = trapDist.ProbabilityDensityFunction(x); //1.1249999999999998
double cdf = trapDist.DistributionFunction(x); //1.28125
string tostr = trapDist.ToString("N2", CultureInfo.InvariantCulture);
Assert.AreEqual(mean, 0.625d, 1e-6);
Assert.AreEqual(variance, 0.37103175d, 1e-6);
Assert.AreEqual(pdf, 1.125, 1e-6, "should match output from dtrapezoid in R");
Assert.AreEqual(cdf, 0.859375, 1e-6);
Assert.AreEqual(tostr, "Trapezoidal(x; a = 0.00, b = 0.33, c = 0.67, d = 1.00, n1 = 2.00, n3 = 2.00, α = 1.00)");
//Verified using R package 'trapezoid'
}
public void DocumentationTest1()
{
#region doc_ctor
// Create a new trapezoidal distribution with linear growth between
// 0 and 2, stability between 2 and 8, and decrease between 8 and 10.
//
//
// +-----------+
// /| |\
// / | | \
// / | | \
// -------+---+-----------+---+-------
// ... 0 2 4 6 8 10 ...
//
var trapz = new TrapezoidalDistribution(a: 0, b: 2, c: 8, d: 10, n1: 1, n3: 1);
double mean = trapz.Mean; // 2.25
double median = trapz.Median; // 5.0
double mode = trapz.Mode; // 4.7706917621394611
double var = trapz.Variance; // 17.986666666666665
double cdf = trapz.DistributionFunction(x: 1.4); // 0.13999999999999999
double pdf = trapz.ProbabilityDensityFunction(x: 1.4); // 0.10000000000000001
double lpdf = trapz.LogProbabilityDensityFunction(x: 1.4); // -2.3025850929940455
double ccdf = trapz.ComplementaryDistributionFunction(x: 1.4); // 0.85999999999999999
double icdf = trapz.InverseDistributionFunction(p: cdf); // 1.3999999999999997
double hf = trapz.HazardFunction(x: 1.4); // 0.11627906976744187
double chf = trapz.CumulativeHazardFunction(x: 1.4); // 0.15082288973458366
string str = trapz.ToString(CultureInfo.InvariantCulture); // Trapezoidal(x; a=0, b=2, c=8, d=10, n1=1, n3=1, α = 1)
#endregion
Assert.AreEqual(2.25, mean);
Assert.AreEqual(5.0, median);
Assert.AreEqual(4.7706917621394611, mode);
Assert.AreEqual(17.986666666666665, var);
Assert.AreEqual(0.15082288973458366, chf);
Assert.AreEqual(0.13999999999999999, cdf);
Assert.AreEqual(0.10000000000000001, pdf);
Assert.AreEqual(-2.3025850929940455, lpdf);
Assert.AreEqual(0.11627906976744187, hf);
Assert.AreEqual(0.85999999999999999, ccdf);
Assert.AreEqual(1.3999999999999997, icdf);
Assert.AreEqual("Trapezoidal(x; a = 0, b = 2, c = 8, d = 10, n1 = 1, n3 = 1, α = 1)", str);
var range1 = trapz.GetRange(0.95);
var range2 = trapz.GetRange(0.99);
var range3 = trapz.GetRange(0.01);
Assert.AreEqual(0.50000000000000044, range1.Min);
Assert.AreEqual(9.5, range1.Max);
Assert.AreEqual(0.10000000000000009, range2.Min);
Assert.AreEqual(9.9, range2.Max);
Assert.AreEqual(0.10000000000000001, range3.Min);
Assert.AreEqual(9.9, range3.Max);
}
public void icdf()
{
var dist = new TrapezoidalDistribution(0, 1, 2, 3, 1, 1);
double[] percentiles = Vector.Range(0.0, 1.0, stepSize: 0.1);
for (int i = 0; i < percentiles.Length; i++)
{
double x = percentiles[i];
double icdf = dist.InverseDistributionFunction(x);
double cdf = dist.DistributionFunction(icdf);
Assert.AreEqual(x, cdf, 1e-5);
}
}
public void rtest()
{
/*
* install.packages('trapezoid')
* library('trapezoid')
*
* ptrapezoid((0:20)/2, min = 0.6, mode1 = 1.2, mode2 = 4.7, max = 6.4)
* dtrapezoid((0:20)/2, min = 0.6, mode1 = 1.2, mode2 = 4.7, max = 6.4)
*/
var dist = new TrapezoidalDistribution(0.6, 1.2, 4.7, 6.4);
Assert.AreEqual(0.00000000, dist.DistributionFunction(0.0));
Assert.AreEqual(0.00000000, dist.DistributionFunction(0.5));
Assert.AreEqual(0.02867384, dist.DistributionFunction(1.0), 1e-6);
Assert.AreEqual(0.12903226, dist.DistributionFunction(1.5), 1e-6);
Assert.AreEqual(0.23655914, dist.DistributionFunction(2.0), 1e-6);
Assert.AreEqual(0.34408602, dist.DistributionFunction(2.5), 1e-6);
Assert.AreEqual(0.45161290, dist.DistributionFunction(3.0), 1e-6);
Assert.AreEqual(0.55913978, dist.DistributionFunction(3.5), 1e-6);
Assert.AreEqual(0.66666667, dist.DistributionFunction(4.0), 1e-6);
Assert.AreEqual(0.77419355, dist.DistributionFunction(4.5), 1e-6);
Assert.AreEqual(0.87602783, dist.DistributionFunction(5.0), 1e-6);
Assert.AreEqual(0.94876660, dist.DistributionFunction(5.5), 1e-6);
Assert.AreEqual(0.98987982, dist.DistributionFunction(6.0), 1e-6);
Assert.AreEqual(1.00000000, dist.DistributionFunction(6.5), 1e-6);
Assert.AreEqual(1.00000000, dist.DistributionFunction(7.0), 1e-6);
Assert.AreEqual(1.00000000, dist.DistributionFunction(7.5), 1e-6);
Assert.AreEqual(1.00000000, dist.DistributionFunction(8.0), 1e-6);
Assert.AreEqual(1.00000000, dist.DistributionFunction(8.5), 1e-6);
Assert.AreEqual(1.00000000, dist.DistributionFunction(9.0), 1e-6);
Assert.AreEqual(1.00000000, dist.DistributionFunction(9.5), 1e-6);
Assert.AreEqual(1.00000000, dist.DistributionFunction(10.0), 1e-6);
Assert.AreEqual(1.00000000, dist.DistributionFunction(10.5));
Assert.AreEqual(0.00000000, dist.ProbabilityDensityFunction(0.0));
Assert.AreEqual(0.00000000, dist.ProbabilityDensityFunction(0.5));
Assert.AreEqual(0.14336918, dist.ProbabilityDensityFunction(1.0), 1e-6);
Assert.AreEqual(0.21505376, dist.ProbabilityDensityFunction(1.5), 1e-6);
Assert.AreEqual(0.21505376, dist.ProbabilityDensityFunction(2.0), 1e-6);
Assert.AreEqual(0.21505376, dist.ProbabilityDensityFunction(2.5), 1e-6);
Assert.AreEqual(0.21505376, dist.ProbabilityDensityFunction(3.0), 1e-6);
Assert.AreEqual(0.21505376, dist.ProbabilityDensityFunction(3.5), 1e-6);
Assert.AreEqual(0.21505376, dist.ProbabilityDensityFunction(4.0), 1e-6);
Assert.AreEqual(0.21505376, dist.ProbabilityDensityFunction(4.5), 1e-6);
Assert.AreEqual(0.17710310, dist.ProbabilityDensityFunction(5.0), 1e-6);
Assert.AreEqual(0.11385199, dist.ProbabilityDensityFunction(5.5), 1e-6);
Assert.AreEqual(0.05060089, dist.ProbabilityDensityFunction(6.0), 1e-6);
Assert.AreEqual(0.00000000, dist.ProbabilityDensityFunction(6.5), 1e-6);
Assert.AreEqual(0.00000000, dist.ProbabilityDensityFunction(7.0), 1e-6);
Assert.AreEqual(0.00000000, dist.ProbabilityDensityFunction(7.5), 1e-6);
Assert.AreEqual(0.00000000, dist.ProbabilityDensityFunction(8.0), 1e-6);
Assert.AreEqual(0.00000000, dist.ProbabilityDensityFunction(8.5), 1e-6);
Assert.AreEqual(0.00000000, dist.ProbabilityDensityFunction(9.0), 1e-6);
Assert.AreEqual(0.00000000, dist.ProbabilityDensityFunction(9.5), 1e-6);
Assert.AreEqual(0.00000000, dist.ProbabilityDensityFunction(10.0), 1e-6);
Assert.AreEqual(0.00000000, dist.ProbabilityDensityFunction(10.5));
}