| public DistributionFunction ( double x ) : double | ||
| x | double | A single point in the distribution range. |
| return | double | |
public override double DistributionFunction(double x)
{
if (x < a)
return 0;
if (x > d)
return 1;
if (x < b)
{
double num = 2 * alpha * (b - a) * n3;
double den = 2 * alpha * (b - a) * n3
+ (alpha + 1) * (c - b) * n1 * n3
+ 2 * (d - c) * n1;
return (num / den) * Math.Pow((x - a) / (b - a), n1);
}
if (x < c)
{
double num = 2 * alpha * (b - a) * n3
+ 2 * (x - b) * n1 * n3 * (1 + ((alpha - 1) * (2 * c - b - x)) / (2 * (c - b)));
double den = 2 * alpha * (b - a) * n3
+ (alpha + 1) * (c - b) * n1 * n3
+ 2 * (c - d) * n1;
return num / den;
}
if (x < d)
{
double num = 2 * (c - d) * n1;
double den = 2 * alpha * (b - a) * n3
+ (alpha + 1) * (c - b) * n1 * n3
+ 2 * (c - d) * n1;
return 1 - num / den * Math.Pow((d - x) / (d - c), n3);
}
return 1;
}
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, 0.00000001);
Assert.AreEqual(variance, 0.37103175d, 0.00000001);
Assert.AreEqual(pdf, 1.125, 0.000000001, "should match output from dtrapezoid in R");
Assert.AreEqual(cdf, 1.28125,0.000000001);
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'
}
