/// <summary>
/// Computes the cumulative distribution function for distributions
/// up to two dimensions. For more than two dimensions, this method
/// is not supported.
/// </summary>
///
public override double DistributionFunction(params double[] x)
{
if (Dimension == 1)
{
double stdDev = Math.Sqrt(Covariance[0, 0]);
if (stdDev == 0)
{
return((x[0] == mean[0]) ? 1 : 0);
}
double z = (x[0] - mean[0]) / stdDev;
return(Normal.Function(z));
}
if (Dimension == 2)
{
double sigma1 = Math.Sqrt(Covariance[0, 0]);
double sigma2 = Math.Sqrt(Covariance[1, 1]);
double rho = Covariance[0, 1] / (sigma1 * sigma2);
if (Double.IsNaN(rho))
{
return((x.IsEqual(mean)) ? 1 : 0);
}
double z = (x[0] - mean[0]) / sigma1;
double w = (x[1] - mean[1]) / sigma2;
return(Normal.Bivariate(z, w, rho));
}
throw new NotSupportedException("The cumulative distribution "
+ "function is only available for up to two dimensions.");
}
public void BivariateFunctionTest()
{
{
double a = Normal.Bivariate(+0, +0, 0.0);
double b = Normal.Bivariate(-1, +0, 0.0);
double c = Normal.Bivariate(+0, -1, 0.0);
double d = Normal.Bivariate(-1, -1, 0.0);
Assert.AreEqual(a, 0.25);
Assert.AreEqual(b, 0.07932762696572859, 1e-10);
Assert.AreEqual(c, 0.07932762696572859, 1e-10);
Assert.AreEqual(d, 0.02517148960005514, 1e-10);
}
{
double a = Normal.Bivariate(0, 0, 0.0);
double b = Normal.Bivariate(1, 0, 0.0);
double c = Normal.Bivariate(0, 1, 0.0);
double d = Normal.Bivariate(1, 1, 0.0);
Assert.AreEqual(a, 0.25);
Assert.AreEqual(b, 0.4206723730342714, 1e-10);
Assert.AreEqual(c, 0.4206723730342714, 1e-10);
Assert.AreEqual(d, 0.707860981737141, 1e-10);
}
{
double a = Normal.Bivariate(+0, +0, 0.99);
double b = Normal.Bivariate(-1, +0, 0.99);
double c = Normal.Bivariate(+0, -1, 0.99);
double d = Normal.Bivariate(-1, -1, 0.99);
Assert.AreEqual(a, 0.477473293177794, 1e-6);
Assert.AreEqual(b, 0.1586552539314527, 1e-10);
Assert.AreEqual(c, 0.1586552539314527, 1e-10);
Assert.AreEqual(d, 0.1450035348479944, 1e-8);
}
{
double a = Normal.Bivariate(0, 0, 0.99);
double b = Normal.Bivariate(1, 0, 0.99);
double c = Normal.Bivariate(0, 1, 0.99);
double d = Normal.Bivariate(1, 1, 0.99);
Assert.AreEqual(a, 0.477473293177794, 1e-6);
Assert.AreEqual(b, 0.4999999999999956, 1e-10);
Assert.AreEqual(c, 0.4999999999999956, 1e-10);
Assert.AreEqual(d, 0.8276930269850803, 1e-8);
}
{
double a = Normal.Bivariate(0, 0, 0.42);
double b = Normal.Bivariate(0, 1, 0.42);
double c = Normal.Bivariate(1, 0, 0.42);
double d = Normal.Bivariate(1, 1, 0.42);
double e = Normal.Bivariate(-0, -1, 0.42);
double f = Normal.Bivariate(-1, -0, 0.42);
double g = Normal.Bivariate(-1, -1, 0.42);
Assert.AreEqual(a, 0.3189849652491711, 1e-10);
Assert.AreEqual(b, 0.4611405565191831, 1e-10);
Assert.AreEqual(c, 0.4611405565191831, 1e-10);
Assert.AreEqual(d, 0.7379699765574815, 1e-10);
Assert.AreEqual(e, 0.1197958104506402, 1e-10);
Assert.AreEqual(f, 0.1197958104506402, 1e-10);
Assert.AreEqual(g, 0.05528048442039563, 1e-10);
}
}
