private static void checkDegenerate(MultivariateNormalDistribution target)
{
Assert.AreEqual(1, target.Mean[0]);
Assert.AreEqual(2, target.Mean[1]);
Assert.AreEqual(0, target.Covariance[0, 0]);
Assert.AreEqual(0, target.Covariance[0, 1]);
Assert.AreEqual(0, target.Covariance[1, 0]);
Assert.AreEqual(0, target.Covariance[1, 1]);
// Common measures
double[] mean = target.Mean; // { 1, 2 }
double[] median = target.Median; // { 4, 2 }
double[] var = target.Variance; // { 0.0, 0.0 } (diagonal from cov)
double[,] cov = target.Covariance; // { { 0.0, 0.0 }, { 0.0, 0.0 } }
// Probability mass functions
double pdf1 = target.ProbabilityDensityFunction(new double[] { 1, 2 });
double pdf2 = target.ProbabilityDensityFunction(new double[] { 4, 2 });
double pdf3 = target.ProbabilityDensityFunction(new double[] { 3, 7 });
double lpdf = target.LogProbabilityDensityFunction(new double[] { 3, 7 });
// Cumulative distribution function (for up to two dimensions)
double cdf1 = target.DistributionFunction(new double[] { 1, 2 });
double cdf2 = target.DistributionFunction(new double[] { 3, 5 });
double ccdf1 = target.ComplementaryDistributionFunction(new double[] { 1, 2 });
double ccdf2 = target.ComplementaryDistributionFunction(new double[] { 3, 5 });
Assert.AreEqual(1, mean[0]);
Assert.AreEqual(2, mean[1]);
Assert.AreEqual(1, median[0]);
Assert.AreEqual(2, median[1]);
Assert.AreEqual(0.0, var[0]);
Assert.AreEqual(0.0, var[1]);
Assert.AreEqual(0.0, cov[0, 0]);
Assert.AreEqual(0.0, cov[0, 1]);
Assert.AreEqual(0.0, cov[1, 0]);
Assert.AreEqual(0.0, cov[1, 1]);
Assert.AreEqual(0.15915494309189532, pdf1);
Assert.AreEqual(0.15915494309189532, pdf2);
Assert.AreEqual(0.15915494309189532, pdf3);
Assert.AreEqual(-1.8378770664093456, lpdf);
Assert.AreEqual(1.0, cdf1);
Assert.AreEqual(0.0, cdf2);
Assert.AreEqual(0.0, ccdf1);
Assert.AreEqual(1.0, ccdf2);
}
public void FitTest3()
{
double[][] observations =
{
new double[] { 1, 2 },
new double[] { 2, 4 },
new double[] { 3, 6 },
new double[] { 4, 8 }
};
var target = new MultivariateNormalDistribution(2);
NormalOptions options = new NormalOptions()
{
Robust = true
};
target.Fit(observations, options);
double pdf = target.ProbabilityDensityFunction(4, 2);
double cdf = target.DistributionFunction(4, 2);
bool psd = target.Covariance.IsPositiveDefinite();
Assert.AreEqual(0.043239154739844896, pdf);
Assert.AreEqual(0.12263905840338646, cdf);
Assert.IsFalse(psd);
}
public void CumulativeFunctionTest2()
{
double[] mean = { 4.2 };
double[,] covariance = { { 1.4 } };
var baseline = new NormalDistribution(4.2, System.Math.Sqrt(covariance[0, 0]));
var target = new MultivariateNormalDistribution(mean, covariance);
for (int i = 0; i < 10; i++)
{
double x = (i - 2) / 10.0;
{
double actual = target.ProbabilityDensityFunction(x);
double expected = baseline.ProbabilityDensityFunction(x);
Assert.AreEqual(expected, actual, 1e-10);
}
{
double actual = target.DistributionFunction(x);
double expected = baseline.DistributionFunction(x);
Assert.AreEqual(expected, actual);
}
{
double actual = target.ComplementaryDistributionFunction(x);
double expected = baseline.ComplementaryDistributionFunction(x);
Assert.AreEqual(expected, actual);
}
}
}
public void CumulativeFunctionTest1()
{
// Comparison against dmvnorm from the mvtnorm R package
double[] mean = { 1, -1 };
double[,] covariance =
{
{ 0.9, 0.4 },
{ 0.4, 0.3 },
};
var target = new MultivariateNormalDistribution(mean, covariance);
double[] x = { 1.2, -0.8 };
// dmvnorm(x=c(1.2, -0.8), mean=c(1, -1), sigma=matrix(c(0.9, 0.4, 0.4, 0.3), 2, 2))
double pdf = target.ProbabilityDensityFunction(x);
// pmvnorm(upper=c(1.2, -0.8), mean=c(1, -1), sigma=matrix(c(0.9, 0.4, 0.4, 0.3), 2, 2))
double cdf = target.DistributionFunction(x);
// pmvnorm(lower=c(1.2, -0.8), mean=c(1, -1), sigma=matrix(c(0.9, 0.4, 0.4, 0.3), 2, 2))
double ccdf = target.ComplementaryDistributionFunction(x);
Assert.AreEqual(0.44620942136345987, pdf);
Assert.AreEqual(0.5049523013014460826, cdf, 1e-10);
Assert.AreEqual(0.27896707550525140507, ccdf, 1e-10);
}
public void ConstructorTest4()
{
// Create a multivariate Gaussian distribution
var dist = new MultivariateNormalDistribution(
// mean vector mu
mean: new double[]
{
4, 2
},
// covariance matrix sigma
covariance: new double[, ]
{
{ 0.3, 0.1 },
{ 0.1, 0.7 }
}
);
// Common measures
double[] mean = dist.Mean; // { 4, 2 }
double[] median = dist.Median; // { 4, 2 }
double[] var = dist.Variance; // { 0.3, 0.7 } (diagonal from cov)
double[,] cov = dist.Covariance; // { { 0.3, 0.1 }, { 0.1, 0.7 } }
// Probability mass functions
double pdf1 = dist.ProbabilityDensityFunction(new double[] { 2, 5 });
double pdf2 = dist.ProbabilityDensityFunction(new double[] { 4, 2 });
double pdf3 = dist.ProbabilityDensityFunction(new double[] { 3, 7 });
double lpdf = dist.LogProbabilityDensityFunction(new double[] { 3, 7 });
// Cumulative distribution function (for up to two dimensions)
// compared against R package mnormt: install.packages("mnormt")
// pmnorm(c(3,5), mean=c(4,2), varcov=matrix(c(0.3,0.1,0.1,0.7), 2,2))
double cdf = dist.DistributionFunction(new double[] { 3, 5 });
double ccdf = dist.ComplementaryDistributionFunction(new double[] { 3, 5 });
Assert.AreEqual(4, mean[0]);
Assert.AreEqual(2, mean[1]);
Assert.AreEqual(4, median[0]);
Assert.AreEqual(2, median[1]);
Assert.AreEqual(0.3, var[0]);
Assert.AreEqual(0.7, var[1]);
Assert.AreEqual(0.3, cov[0, 0]);
Assert.AreEqual(0.1, cov[0, 1]);
Assert.AreEqual(0.1, cov[1, 0]);
Assert.AreEqual(0.7, cov[1, 1]);
Assert.AreEqual(0.000000018917884164743237, pdf1);
Assert.AreEqual(0.35588127170858852, pdf2);
Assert.AreEqual(0.000000000036520107734505265, pdf3);
Assert.AreEqual(-24.033158110192296, lpdf);
Assert.AreEqual(0.033944035782101548, cdf);
}
public void ConstructorTest1()
{
NormalDistribution normal = new NormalDistribution(4.2, 1.2);
MultivariateNormalDistribution target = new MultivariateNormalDistribution(new[] { 4.2 }, new[, ] {
{ 1.2 * 1.2 }
});
double[] mean = target.Mean;
double[] median = target.Median;
double[] var = target.Variance;
double[,] cov = target.Covariance;
double apdf1 = target.ProbabilityDensityFunction(new double[] { 2 });
double apdf2 = target.ProbabilityDensityFunction(new double[] { 4 });
double apdf3 = target.ProbabilityDensityFunction(new double[] { 3 });
double alpdf = target.LogProbabilityDensityFunction(new double[] { 3 });
double acdf = target.DistributionFunction(new double[] { 3 });
double accdf = target.ComplementaryDistributionFunction(new double[] { 3 });
double epdf1 = target.ProbabilityDensityFunction(new double[] { 2 });
double epdf2 = target.ProbabilityDensityFunction(new double[] { 4 });
double epdf3 = target.ProbabilityDensityFunction(new double[] { 3 });
double elpdf = target.LogProbabilityDensityFunction(new double[] { 3 });
double ecdf = target.DistributionFunction(new double[] { 3 });
double eccdf = target.ComplementaryDistributionFunction(new double[] { 3 });
Assert.AreEqual(normal.Mean, target.Mean[0]);
Assert.AreEqual(normal.Median, target.Median[0]);
Assert.AreEqual(normal.Variance, target.Variance[0]);
Assert.AreEqual(normal.Variance, target.Covariance[0, 0]);
Assert.AreEqual(epdf1, apdf1);
Assert.AreEqual(epdf2, apdf2);
Assert.AreEqual(epdf3, apdf3);
Assert.AreEqual(elpdf, alpdf);
Assert.AreEqual(ecdf, acdf);
Assert.AreEqual(eccdf, accdf);
Assert.AreEqual(1.0 - ecdf, eccdf);
}
public static double CBND(double X, double Y, double rho)
{
double[] _mean = new double[] { 0.0, 0.0 };
double[,] _convariance = new double[, ] {
{ 1.0, rho }, { rho, 1.0 }
};
var dist = new MultivariateNormalDistribution(_mean, _convariance);
double[] para = { X, Y };
double cdf = dist.DistributionFunction(para);
return(cdf);
}
