/// <summary>
/// Sets properties and attributes of class in accordance with XML definition.
/// </summary>
/// <param name="Definition">XML definition</param>
public override Task FromXml(XmlElement Definition)
{
this.t0 = XML.Attribute(Definition, "t0", 0.0);
this.k = XML.Attribute(Definition, "k", 0.0);
this.kHalf = this.k / 2;
this.c = 1.0 / StatMath.Γ(this.kHalf);
return(base.FromXml(Definition));
}
public void Test_01_Γ()
{
// https://dlmf.nist.gov/5.4
Assert.IsTrue(Math.Abs(StatMath.Γ(1) - 1) < 1e-10);
Assert.IsTrue(Math.Abs(StatMath.Γ(1.0 / 2) - 1.77245385090551602729) < 1e-10);
Assert.IsTrue(Math.Abs(StatMath.Γ(1.0 / 3) - 2.67893853470774763365) < 1e-10);
Assert.IsTrue(Math.Abs(StatMath.Γ(2.0 / 3) - 1.35411793942640041694) < 1e-10);
Assert.IsTrue(Math.Abs(StatMath.Γ(1.0 / 4) - 3.62560990822190831193) < 1e-10);
Assert.IsTrue(Math.Abs(StatMath.Γ(3.0 / 4) - 1.22541670246517764512) < 1e-10);
}
/// <summary>
/// The Cumulative Distribution Function (CDF) of the distribution, excluding intensity (<see cref="Distribution.N"/>).
/// </summary>
/// <param name="t">Time</param>
/// <param name="NrCycles">Number of time cycles completed.</param>
/// <returns>CDU(t)</returns>
protected override double GetCumulativeProbability(double t, int NrCycles)
{
t -= this.t0;
if (t < 0)
{
return(0);
}
else
{
return(StatMath.γ(this.kHalf, t * t / 2) * this.c);
}
}
/// <summary>
/// The Cumulative Distribution Function (CDF) of the distribution, excluding intensity (<see cref="Distribution.N"/>).
/// </summary>
/// <param name="t">Time</param>
/// <param name="NrCycles">Number of time cycles completed.</param>
/// <returns>CDU(t)</returns>
protected override double GetCumulativeProbability(double t, int NrCycles)
{
t -= this.t0;
if (t < 0)
{
return(0);
}
else
{
return(StatMath.γ(this.α, this.β * t) * this.invGammaAlpha);
}
}
/// <summary>
/// The Cumulative Distribution Function (CDF) of the distribution, excluding intensity (<see cref="Distribution.N"/>).
/// </summary>
/// <param name="t">Time</param>
/// <param name="NrCycles">Number of time cycles completed.</param>
/// <returns>CDU(t)</returns>
protected override double GetCumulativeProbability(double t, int NrCycles)
{
if (Math.Abs(t - this.μ) > Math.Abs(this.TimeCycleUnits + t - this.μ))
{
t += this.TimeCycleUnits;
NrCycles--;
}
double x = (t - this.μ) / this.σSqrt2;
double erf = x < -5 ? -1 : x > 5 ? 1 : StatMath.Erf(x);
return(((1 + erf) / 2) + NrCycles);
}
/// <summary>
/// Sets properties and attributes of class in accordance with XML definition.
/// </summary>
/// <param name="Definition">XML definition</param>
public override Task FromXml(XmlElement Definition)
{
this.t0 = XML.Attribute(Definition, "t0", 0.0);
if (Definition.HasAttribute("k") && Definition.HasAttribute("θ"))
{
this.k = XML.Attribute(Definition, "k", 0.0);
this.θ = XML.Attribute(Definition, "θ", 0.0);
if (Definition.HasAttribute("α") || Definition.HasAttribute("β") || Definition.HasAttribute("μ"))
{
throw new Exception("Too many parameters in Gamma distribution definition.");
}
this.α = this.k;
this.β = 1 / this.θ;
this.μ = this.k * this.θ;
}
else if (Definition.HasAttribute("α") && Definition.HasAttribute("β"))
{
this.α = XML.Attribute(Definition, "α", 0.0);
this.β = XML.Attribute(Definition, "β", 0.0);
if (Definition.HasAttribute("k") || Definition.HasAttribute("θ") || Definition.HasAttribute("μ"))
{
throw new Exception("Too many parameters in Gamma distribution definition.");
}
this.k = this.α;
this.θ = 1 / this.β;
this.μ = this.α / this.β;
}
else if (Definition.HasAttribute("k") && Definition.HasAttribute("μ"))
{
this.k = XML.Attribute(Definition, "k", 0.0);
this.μ = XML.Attribute(Definition, "μ", 0.0);
if (Definition.HasAttribute("α") || Definition.HasAttribute("β") || Definition.HasAttribute("θ"))
{
throw new Exception("Too many parameters in Gamma distribution definition.");
}
this.α = this.k;
this.β = this.α / this.μ;
this.θ = this.μ / this.k;
}
this.invGammaAlpha = 1.0 / StatMath.Γ(this.α);
return(base.FromXml(Definition));
}
/// <summary>
/// Evaluates the function on two scalar arguments.
/// </summary>
/// <param name="Argument1">Function argument 1.</param>
/// <param name="Argument2">Function argument 2.</param>
/// <param name="Variables">Variables collection.</param>
/// <returns>Function result.</returns>
public override IElement EvaluateScalar(Complex Argument1, Complex Argument2, Variables Variables)
{
return(new ComplexNumber(StatMath.Γ(Argument1, Argument2)));
}
/// <summary>
/// Evaluates the function on two scalar arguments.
/// </summary>
/// <param name="Argument1">Function argument 1.</param>
/// <param name="Argument2">Function argument 2.</param>
/// <param name="Variables">Variables collection.</param>
/// <returns>Function result.</returns>
public override IElement EvaluateScalar(double Argument1, double Argument2, Variables Variables)
{
return(new DoubleNumber(StatMath.Γ(Argument1, Argument2)));
}
/// <summary>
/// Evaluates the function on a scalar argument.
/// </summary>
/// <param name="Argument">Function argument.</param>
/// <param name="Variables">Variables collection.</param>
/// <returns>Function result.</returns>
public override IElement EvaluateScalar(double Argument, Variables Variables)
{
return(new DoubleNumber(StatMath.Erf(Argument)));
}
