public void GammaFitTest()
{
double k0 = 0.05;
double t0 = 2.0;
GammaDistribution G = new GammaDistribution(k0, t0);
Random rng = new Random(1);
Sample S = new Sample();
for (int i = 0; i < 1000; i++)
{
S.Add(G.GetRandomValue(rng));
}
Console.WriteLine("mean sample={0} distribution={1}", S.Mean, G.Mean);
Console.WriteLine("variance sample={0} distribution={1}", S.Variance, G.Variance);
Console.WriteLine("moment estimate k={0} t={1}", S.Mean * S.Mean / S.Variance, S.Variance / S.Mean);
double q = 0;
foreach (double x in S)
{
q += Math.Log(x / S.Mean);
}
q /= S.Count;
q = -q;
Console.WriteLine("q = {0}, Log(k)-Psi(k)={1}", q, Math.Log(k0) - AdvancedMath.Psi(k0));
double ke0 = S.Mean * S.Mean / S.Variance;
Console.WriteLine("ke0={0} Log(ke0)-Psi(ke0)={1}", ke0, Math.Log(ke0) - AdvancedMath.Psi(ke0));
double ke1 = 1.0 / (2.0 * q - 2.0 / 3.0 * q * q + 4.0 / 9.0 * q * q * q - 14.0 / 135.0 * q * q * q * q);
Console.WriteLine("ke1={0} Log(ke1)-Psi(ke1)={1}", ke1, Math.Log(ke1) - AdvancedMath.Psi(ke1));
double ke2 = 1.0 / (q - AdvancedMath.EulerGamma);
Console.WriteLine("ke2={0} Log(ke2)-Psi(ke2)={1}", ke2, Math.Log(ke2) - AdvancedMath.Psi(ke2));
}