| public DistributionFunction ( double x ) : double | ||
| x | double | /// A single point in the distribution range. |
| return | double | |
/// <summary>
/// Gets the cumulative distribution function (cdf) for
/// this distribution evaluated at point <c>k</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <remarks>
/// The Cumulative Distribution Function (CDF) describes the cumulative
/// probability that a given value or any value smaller than it will occur.
/// </remarks>
///
protected internal override double InnerDistributionFunction(double x)
{
if (this.exact)
{
return(exactMethod(x, table));
}
if (Correction == ContinuityCorrection.Midpoint)
{
if (x > Mean)
{
x = x - 0.5;
}
else
{
x = x + 0.5;
}
}
else if (Correction == ContinuityCorrection.KeepInside)
{
x = x + 0.5;
}
return(approximation.DistributionFunction(x));
}
private double distributionFunction(double x)
{
if (exact)
{
// For small samples (< 30) and if there are not very large
// differences in samples sizes, this distribution is exact.
return(WilcoxonDistribution.exactMethod(x, table));
}
if (Correction == ContinuityCorrection.Midpoint)
{
if (x > Mean)
{
x = x - 0.5;
}
else
{
x = x + 0.5;
}
}
else if (Correction == ContinuityCorrection.KeepInside)
{
x = x + 0.5;
}
return(approximation.DistributionFunction(x));
}
/// <summary>
/// Gets the cumulative distribution function (cdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <remarks>
/// The Cumulative Distribution Function (CDF) describes the cumulative
/// probability that a given value or any value smaller than it will occur.
/// </remarks>
///
/// <example>
/// See <see cref="KolmogorovSmirnovDistribution"/>.
/// </example>
///
public override double DistributionFunction(double x)
{
if (x <= 0)
{
return(1);
}
if (x >= 1)
{
return(0);
}
double z = g(x);
double cdf = normal.DistributionFunction(z);
return(cdf);
}
/// <summary>
/// Gets the complementary cumulative distribution function
/// (ccdf) for this distribution evaluated at point <c>x</c>.
/// This function is also known as the Survival function.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <remarks>
/// The Complementary Cumulative Distribution Function (CCDF) is
/// the complement of the Cumulative Distribution Function, or 1
/// minus the CDF.
/// </remarks>
///
protected internal override double InnerComplementaryDistributionFunction(double x)
{
double z = g(x);
return(normal.DistributionFunction(z));
}
public void DistributionFunctionTest1()
{
var target = GeneralizedNormalDistribution.Normal(mean: 0.42, stdDev: 4.2);
var normal = new NormalDistribution(mean: 0.42, stdDev: 4.2);
for (double x = -10; x < 10; x += 0.0001)
{
double actual = target.DistributionFunction(x);
double expected = normal.DistributionFunction(x);
Assert.AreEqual(expected, actual, 1e-10);
Assert.IsFalse(Double.IsNaN(actual));
}
}
public void ConstructorTest2()
{
var original = new NormalDistribution(mean: 4, stdDev: 4.2);
var normal = GeneralContinuousDistribution.FromDensityFunction(
original.Support, original.ProbabilityDensityFunction);
for (double i = -10; i < +10; i += 0.1)
{
double expected = original.DistributionFunction(i);
double actual = normal.DistributionFunction(i);
double diff = Math.Abs(expected - actual) / expected;
Assert.IsTrue(diff < 1e-7);
}
testNormal(normal, 1);
}
public void DistributionFunctionTest3()
{
double expected, actual;
// Test small variance
NormalDistribution target = new NormalDistribution(1.0, double.Epsilon);
expected = 0;
actual = target.DistributionFunction(0);
Assert.AreEqual(expected, actual);
expected = 0.5;
actual = target.DistributionFunction(1.0);
Assert.AreEqual(expected, actual);
expected = 1.0;
actual = target.DistributionFunction(1.0 + 1e-15);
Assert.AreEqual(expected, actual);
expected = 0.0;
actual = target.DistributionFunction(1.0 - 1e-15);
Assert.AreEqual(expected, actual);
}
public void DistributionFunctionTest()
{
double x = 3;
double mean = 7;
double dev = 5;
NormalDistribution target = new NormalDistribution(mean, dev);
double expected = 0.211855398583397;
double actual = target.DistributionFunction(x);
Assert.IsFalse(double.IsNaN(actual));
Assert.AreEqual(expected, actual, 1e-15);
}
/// <summary>
/// Gets the cumulative distribution function (cdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <remarks>
/// The Cumulative Distribution Function (CDF) describes the cumulative
/// probability that a given value or any value smaller than it will occur.
/// </remarks>
///
/// <example>
/// See <see cref="KolmogorovSmirnovDistribution"/>.
/// </example>
///
public override double DistributionFunction(double x)
{
return(normal.DistributionFunction(g(x)));
}