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)));
}
}
/// <inheritdoc />
public override double LeftProbability(double x)
{
if (x <= 0.0)
{
return(0.0);
}
else
{
return(normal.LeftProbability(Math.Log(x)));
}
}
/// <inheritdoc />
public override double LeftProbability(double x)
{
if (x <= 0.0)
{
return(0.0);
}
else
{
return(normal.LeftProbability(Math.Log(x)));
}
/*
* double z = (Math.Log(x) - mu) / sigma;
* return (NormalDistribution.Phi(z));
*/
}
public void TestNormalOrderStatistic()
{
int n = 100;
//int r = 3 * n / 4;
int r = 52;
Distribution d = new NormalDistribution();
double C = Math.Exp(AdvancedIntegerMath.LogFactorial(n) - AdvancedIntegerMath.LogFactorial(r - 1) - AdvancedIntegerMath.LogFactorial(n - r));
double m = GaussHermiteIntegrate(x => C * MoreMath.Pow(d.LeftProbability(x), r - 1) * MoreMath.Pow(d.RightProbability(x), n - r) * x);
//double m = GaussHermiteIntegrate(x => 1.0);
double m2 = FunctionMath.Integrate(
//x => 1.0 * Math.Exp(-x * x / 2.0) / Math.Sqrt(2.0 * Math.PI),
x => C * MoreMath.Pow(d.LeftProbability(x), r - 1) * MoreMath.Pow(d.RightProbability(x), n - r) * x * Math.Exp(-x * x / 2.0) / Math.Sqrt(2.0 * Math.PI),
Interval.FromEndpoints(Double.NegativeInfinity, Double.PositiveInfinity)
);
Console.WriteLine(m);
Console.WriteLine(m2);
Console.WriteLine(NormalMeanOrderStatisticExpansion(r, n));
Console.WriteLine(NormalMeanOrderStatisticExpansion2(r, n));
//Console.WriteLine(1.5 / Math.Sqrt(Math.PI));
}
