public void TestMethod1()
{
Distribution n0 = new TransformedDistribution(new NormalDistribution(), -2.0, 3.0);
Distribution n1 = new NormalDistribution(-2.0, 3.0);
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.Mean, n1.Mean));
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.Variance, n1.Variance));
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.StandardDeviation, n1.StandardDeviation));
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.Skewness, n1.Skewness));
for (int k = 0; k < 8; k++) {
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.Moment(k), n1.Moment(k)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.MomentAboutMean(k), n1.MomentAboutMean(k)));
}
foreach (double x in TestUtilities.GenerateUniformRealValues(-8.0, 8.0, 8)) {
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.ProbabilityDensity(x), n1.ProbabilityDensity(x)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.LeftProbability(x), n1.LeftProbability(x)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.RightProbability(x), n1.RightProbability(x)));
}
foreach (double P in TestUtilities.GenerateRealValues(1.0E-4, 1.0, 4)) {
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.InverseLeftProbability(P), n1.InverseLeftProbability(P)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(n0.InverseRightProbability(P), n1.InverseRightProbability(P)));
}
}
public MultivariateSample CreateMultivariateNormalSample(ColumnVector M, SymmetricMatrix C, int n)
{
int d = M.Dimension;
MultivariateSample S = new MultivariateSample(d);
SquareMatrix A = C.CholeskyDecomposition().SquareRootMatrix();
Random rng = new Random(1);
Distribution normal = new NormalDistribution();
for (int i = 0; i < n; i++) {
// create a vector of normal deviates
ColumnVector V = new ColumnVector(d);
for (int j = 0; j < d; j++) {
double y = rng.NextDouble();
double z = normal.InverseLeftProbability(y);
V[j] = z;
}
// form the multivariate distributed vector
ColumnVector X = M + A * V;
// add it to the sample
S.Add(X);
}
return (S);
}
/// <inheritdoc />
public override double InverseLeftProbability(double P)
{
if ((P < 0.0) || (P > 1.0))
{
throw new ArgumentOutOfRangeException(nameof(P));
}
return(Math.Exp(normal.InverseLeftProbability(P)));
}
/// <inheritdoc />
public override double InverseLeftProbability(double P)
{
if ((P < 0.0) || (P > 1.0))
{
throw new ArgumentOutOfRangeException("P");
}
return(Math.Exp(normal.InverseLeftProbability(P)));
/*
* double z = Global.SqrtTwo * AdvancedMath.InverseErf(2.0 * P - 1.0);
* return (Math.Exp(mu + sigma * z));
*/
}
public void StudentTest2()
{
// make sure Student t is consistent with its definition
// we are going to take a sample that we expect to be t-distributed
Sample tSample = new Sample();
// begin with an underlying normal distribution
Distribution xDistribution = new NormalDistribution();
// compute a bunch of t satistics from the distribution
for (int i = 0; i < 100000; i++) {
// take a small sample from the underlying distribution
// (as the sample gets large, the t distribution becomes normal)
Random rng = new Random(314159+i);
double p = xDistribution.InverseLeftProbability(rng.NextDouble());
double q = 0.0;
for (int j = 0; j < 5; j++) {
double x = xDistribution.InverseLeftProbability(rng.NextDouble());
q += x * x;
}
q = q / 5;
double t = p / Math.Sqrt(q);
tSample.Add(t);
}
Distribution tDistribution = new StudentDistribution(5);
TestResult result = tSample.KolmogorovSmirnovTest(tDistribution);
Console.WriteLine(result.LeftProbability);
}
public void StudentTest()
{
// make sure Student t is consistent with its definition
// we are going to take a sample that we expect to be t-distributed
Sample tSample = new Sample();
// begin with an underlying normal distribution
Distribution xDistribution = new NormalDistribution(1.0, 2.0);
// compute a bunch of t satistics from the distribution
for (int i = 0; i < 200000; i++) {
// take a small sample from the underlying distribution
// (as the sample gets large, the t distribution becomes normal)
Random rng = new Random(i);
Sample xSample = new Sample();
for (int j = 0; j < 5; j++) {
double x = xDistribution.InverseLeftProbability(rng.NextDouble());
xSample.Add(x);
}
// compute t for the sample
double t = (xSample.Mean - xDistribution.Mean) / (xSample.PopulationStandardDeviation.Value / Math.Sqrt(xSample.Count));
tSample.Add(t);
//Console.WriteLine(t);
}
// t's should be t-distrubuted; use a KS test to check this
Distribution tDistribution = new StudentDistribution(4);
TestResult result = tSample.KolmogorovSmirnovTest(tDistribution);
Console.WriteLine(result.LeftProbability);
//Assert.IsTrue(result.LeftProbability < 0.95);
// t's should be demonstrably not normally distributed
Console.WriteLine(tSample.KolmogorovSmirnovTest(new NormalDistribution()).LeftProbability);
//Assert.IsTrue(tSample.KolmogorovSmirnovTest(new NormalDistribution()).LeftProbability > 0.95);
}
public void TestNormal()
{
NormalDistribution n = new NormalDistribution();
Console.WriteLine(n.InverseLeftProbability(1.0E-10));
Console.WriteLine(n.InverseRightProbability(1.0E-10));
Console.WriteLine(n.InverseLeftProbability(1.0E-300));
Console.WriteLine(n.InverseRightProbability(1.0E-300));
Console.WriteLine(n.InverseLeftProbability(1.0));
//Console.WriteLine(n.InverseLeftProbability(0.26));
}
public void TestBeta()
{
double a = 200.0; double b = 200.0; double P = 1.0E-5;
double x1 = ApproximateInverseBetaSeries(a, b, P);
if ((0.0 < x1) && (x1 < 1.0)) {
Console.WriteLine("x1 {0} {1}", x1, AdvancedMath.LeftRegularizedBeta(a, b, x1));
}
double x2 = 1.0 - ApproximateInverseBetaSeries(b, a, 1.0 - P);
if ((0.0 < x2) && (x2 < 1.0)) {
Console.WriteLine("x2 {0} {1}", x2, AdvancedMath.LeftRegularizedBeta(a, b, x2));
}
//x1 = RefineInverseBeta(a, b, P, x1);
//Console.WriteLine("{0} {1}", x1, AdvancedMath.LeftRegularizedBeta(a, b, x1));
NormalDistribution N = new NormalDistribution();
double m = a / (a + b); double s = Math.Sqrt(a * b / (a + b + 1.0)) / (a + b);
double x3 = m + s * N.InverseLeftProbability(P);
if ((0.0 < x3) && (x3 < 1.0)) {
Console.WriteLine("x3 {0} {1}", x3, AdvancedMath.LeftRegularizedBeta(a, b, x3));
}
//Console.WriteLine(AdvancedMath.Beta(a, b, 0.35) / AdvancedMath.Beta(a, b));
//Console.WriteLine(AdvancedMath.Beta(a, b, 0.40) / AdvancedMath.Beta(a, b));
//Console.WriteLine(AdvancedMath.Beta(a, b, 0.45) / AdvancedMath.Beta(a, b));
}
public void MultivariateLinearRegressionTest()
{
// define model y = a + b0 * x0 + b1 * x1 + noise
double a = 1.0;
double b0 = -2.0;
double b1 = 3.0;
Distribution noise = new NormalDistribution(0.0, 10.0);
// draw a sample from the model
Random rng = new Random(1);
MultivariateSample sample = new MultivariateSample(3);
for (int i = 0; i < 100; i++) {
double x0 = -10.0 + 20.0 * rng.NextDouble();
double x1 = -10.0 + 20.0 * rng.NextDouble();
double eps = noise.InverseLeftProbability(rng.NextDouble());
double y = a + b0 * x0 + b1 * x1 + eps;
sample.Add(x0, x1, y);
}
// do a linear regression fit on the model
FitResult result = sample.LinearRegression(2);
// the result should have the appropriate dimension
Assert.IsTrue(result.Dimension == 3);
// the result should be significant
Console.WriteLine("{0} {1}", result.GoodnessOfFit.Statistic, result.GoodnessOfFit.LeftProbability);
Assert.IsTrue(result.GoodnessOfFit.LeftProbability > 0.95);
// the parameters should match the model
Console.WriteLine(result.Parameter(0));
Assert.IsTrue(result.Parameter(0).ConfidenceInterval(0.90).ClosedContains(b0));
Console.WriteLine(result.Parameter(1));
Assert.IsTrue(result.Parameter(1).ConfidenceInterval(0.90).ClosedContains(b1));
Console.WriteLine(result.Parameter(2));
Assert.IsTrue(result.Parameter(2).ConfidenceInterval(0.90).ClosedContains(a));
}
public void TimeNormalGenerators()
{
Random rng = new Random(1);
//IDeviateGenerator nRng = new BoxMullerNormalGenerator();
//IDeviateGenerator nRng = new PolarRejectionNormalDeviateGenerator();
//IDeviateGenerator nRng = new RatioOfUniformsNormalGenerator();
IDeviateGenerator nRng = new LevaNormalGenerator();
//Sample sample = new Sample();
Distribution nrm = new NormalDistribution();
Stopwatch timer = Stopwatch.StartNew();
double sum = 0.0;
for (int i = 0; i < 10000000; i++) {
sum += nrm.InverseLeftProbability(rng.NextDouble());
//sum += nRng.GetNext(rng);
//sample.Add(nRng.GetNext(rng));
}
timer.Stop();
//Console.WriteLine(sample.KolmogorovSmirnovTest(new NormalDistribution()).RightProbability);
Console.WriteLine(sum);
Console.WriteLine(timer.ElapsedMilliseconds);
}