public static double CBivariateStandardNormal(double h, double k, double rho)
{
// Check the limiting cases of perfect correlation and negative correlation
if (rho > 0.99999)
{
return(Distributions.CDistStandardNormal(Math.Min(h, k)));
}
else if (rho < -0.99999)
{
if (k <= -h)
{
return(0.0);
}
else
{
return(Distributions.CDistStandardNormal(h) + Distributions.CDistStandardNormal(k) - 1);
}
}
if (h <= 0 && k <= 0 && rho <= 0)
{
return(CBivariateStandardNormal_UseForNegatives(h, k, rho));
}
else if (h <= 0 && k >= 0 && rho >= 0)
{
return(Distributions.CDistStandardNormal(h) - CBivariateStandardNormal_UseForNegatives(h, -k, -rho));
}
else if (h >= 0 && k <= 0 && rho >= 0)
{
return(Distributions.CDistStandardNormal(k) - CBivariateStandardNormal_UseForNegatives(-h, k, -rho));
}
else if (h >= 0 && k >= 0 && rho <= 0)
{
return(Distributions.CDistStandardNormal(h) + Distributions.CDistStandardNormal(k) - 1 + CBivariateStandardNormal_UseForNegatives(-h, -k, rho));
}
else
{
double denom = Math.Sqrt(h * h - 2 * rho * h * k + k * k);
double rho_hk = (rho * h - k) * Math.Sign(h) / denom;
double rho_kh = (rho * k - h) * Math.Sign(k) / denom;
double delta = (1.0 - Math.Sign(h) * Math.Sign(k)) / 4.0;
return(CBivariateStandardNormal(h, 0, rho_hk) + CBivariateStandardNormal(k, 0, rho_kh) - delta);
}
}
public static void TestHarness()
{
Console.WriteLine("Zero is {0}", CBivariateStandardNormal(-1000, -1000, 0));
Console.WriteLine("{0} is {1}", Distributions.CDistStandardNormal(0), CBivariateStandardNormal(+1000, 0, 0));
Console.WriteLine("{0} is {1}", Distributions.CDistStandardNormal(0.5), CBivariateStandardNormal(+1000, 0.5, 0));
Console.WriteLine("{0} is {1}", Distributions.CDistStandardNormal(-0.5), CBivariateStandardNormal(+1000, -0.5, 0));
Console.WriteLine("{0} is {1}", Distributions.CDistStandardNormal(-0.5), CBivariateStandardNormal(-0.5, -0.5, 1.0));
Console.WriteLine("{0} is {1}", Distributions.CDistStandardNormal(-0.5), CBivariateStandardNormal(-0.5, -0.2, 1.0));
Console.WriteLine("{0} is {1}", Distributions.CDistStandardNormal(-0.2), CBivariateStandardNormal(-0.1, -0.2, 1.0));
Console.WriteLine("{0} is {1}", 0, CBivariateStandardNormal(-0.5, -0.5, -1.0));
Console.WriteLine("{0} is {1}", 0, CBivariateStandardNormal(-0.5, -0.2, -1.0));
Console.WriteLine("{0} is {1}", 0, CBivariateStandardNormal(-0.1, -0.2, -1.0));
Console.WriteLine("{0} is {1}", Distributions.CDistStandardNormal(0.1) + Distributions.CDistStandardNormal(0.5) - 1, CBivariateStandardNormal(0.1, 0.5, -1.0));
Console.WriteLine("Pain is {0}", CBivariateStandardNormal(3.8922701863527047, -0.28284271247461906, -0.70710678118654757));
TestHarness_GUI();
}
public double getProb(Vector a, Vector b, double alpha, double epsilon, int N_max)
{
// A neat reference to match the document
int m = correlation.rows;
Matrix c = correlation_root;
// Check that we are not in univariate land....
if (1 == m)
{
return(Distributions.CDistStandardNormal(b[0]) - Distributions.CDistStandardNormal(a[0]));
}
// Our variables
double[] d = new double[m];
double[] e = new double[m];
double[] f = new double[m];
double[] y = new double[m];
double[] w = new double[m];
// Initialisation code
double intsum = 0.0;
int N = 0;
double varsum = 0.0;
d[0] = Distributions.CDistStandardNormal(a[0] / c[0, 0]);
e[0] = Distributions.CDistStandardNormal(b[0] / c[0, 0]);
f[0] = e[0] - d[0];
double error = 0.0;
do
{
for (int i = 0; i < m - 1; ++i)
{
w[i] = random.NextDouble();
}
for (int i = 1; i < m; ++i)
{
y[i - 1] = Distributions.InvDist_SN(d[i - 1] + w[i - 1] * (e[i - 1] - d[i - 1]));
double sum_cij_yj = 0.0;
for (int j = 0; j <= i - 1; ++j)
{
sum_cij_yj += c[i, j] * y[j];
}
d[i] = Distributions.CDistStandardNormal((a[i] - sum_cij_yj) / c[i, i]);
e[i] = Distributions.CDistStandardNormal((b[i] - sum_cij_yj) / c[i, i]);
f[i] = (e[i] - d[i]) * f[i - 1];
++N;
double delta = (f[m - 1] - intsum) / N;
intsum += delta;
varsum = (N - 2) * varsum / N + delta * delta;
error = alpha * Math.Sqrt(varsum);
}
} while (error > epsilon && N < N_max);
if (N >= N_max)
{
//System.Console.WriteLine("Exceeded");
//throw new GenericException("Reached maximum number of iterations");
}
return(intsum);
}