| public ProbabilityDensityFunction ( double x ) : double | ||
| x | double | A single point in the distribution range. For a /// univariate distribution, this should be a single /// double value. For a multivariate distribution, /// this should be a double array. |
| return | double | |
/// <summary>
/// Gets the probability density function (pdf) for
/// this distribution evaluated at point <c>u</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <returns>
/// The probability of <c>u</c> occurring
/// in the current distribution.
/// </returns>
///
/// <remarks>
/// The Probability Density Function (PDF) describes the
/// probability that a given value <c>u</c> will occur.
/// </remarks>
///
/// <example>
/// See <see cref="MannWhitneyDistribution"/>.
/// </example>
///
protected internal override double InnerProbabilityDensityFunction(double x)
{
if (this.exact)
{
return(WilcoxonDistribution.count(x, table) / (double)table.Length);
}
return(approximation.ProbabilityDensityFunction(x));
}
/// <summary>
/// Gets the probability density function (pdf) for
/// this distribution evaluated at point <c>w</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <returns>
/// The probability of <c>w</c> occurring
/// in the current distribution.
/// </returns>
///
/// <remarks>
/// The Probability Density Function (PDF) describes the
/// probability that a given value <c>x</c> will occur.
/// </remarks>
///
public override double ProbabilityDensityFunction(double x)
{
if (this.exact)
{
return(count(x, table) / (double)table.Length);
}
return(approximation.ProbabilityDensityFunction(x));
}
/// <summary>
/// Gets the probability density function (pdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <returns>
/// The probability of <c>x</c> occurring
/// in the current distribution.
/// </returns>
///
/// <remarks>
/// The Probability Density Function (PDF) describes the
/// probability that a given value <c>x</c> will occur.
/// </remarks>
///
public override double ProbabilityDensityFunction(double x)
{
if (x <= 0 || x >= 1)
{
return(0);
}
double z = g(x);
return(normal.ProbabilityDensityFunction(z));
}
/// <summary>
/// Gets the probability density function (pdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <returns>
/// The probability of <c>x</c> occurring
/// in the current distribution.
/// </returns>
///
/// <remarks>
/// The Probability Density Function (PDF) describes the
/// probability that a given value <c>x</c> will occur.
/// </remarks>
///
protected internal override double InnerProbabilityDensityFunction(double x)
{
double z = g(x);
return(normal.ProbabilityDensityFunction(z));
}
public void ConstructorTest1()
{
var original = new NormalDistribution(mean: 4, stdDev: 4.2);
var normal = GeneralContinuousDistribution.FromDistributionFunction(
original.Support, original.DistributionFunction);
for (double i = -10; i < +10; i += 0.1)
{
double expected = original.ProbabilityDensityFunction(i);
double actual = normal.ProbabilityDensityFunction(i);
double diff = Math.Abs(expected - actual);
Assert.AreEqual(expected, actual, 1e-6);
}
testNormal(normal, 1e3);
}
public void ProbabilityDensityFunctionTest2()
{
double expected, actual;
// Test for small variance
NormalDistribution target = new NormalDistribution(4.2, double.Epsilon);
expected = 0;
actual = target.ProbabilityDensityFunction(0);
Assert.AreEqual(expected, actual);
expected = double.PositiveInfinity;
actual = target.ProbabilityDensityFunction(4.2);
Assert.AreEqual(expected, actual);
}
public void ProbabilityDensityFunctionTest()
{
double x = 3;
double mean = 7;
double dev = 5;
NormalDistribution target = new NormalDistribution(mean, dev);
double expected = 0.0579383105522966;
double actual = target.ProbabilityDensityFunction(x);
Assert.IsFalse(double.IsNaN(actual));
Assert.AreEqual(expected, actual, 1e-15);
}
/// <summary>
/// Gets the probability density function (pdf) for
/// this distribution evaluated at point <c>x</c>.
/// </summary>
///
/// <param name="x">A single point in the distribution range.</param>
///
/// <returns>
/// The probability of <c>x</c> occurring
/// in the current distribution.
/// </returns>
///
/// <remarks>
/// The Probability Density Function (PDF) describes the
/// probability that a given value <c>x</c> will occur.
/// </remarks>
///
public override double ProbabilityDensityFunction(double x)
{
return(normal.ProbabilityDensityFunction(g(x)));
}
public void InfiniteGaussKronrodTest()
{
NormalDistribution norm;
for (int i = -10; i < 10; i++)
{
norm = new NormalDistribution(i, 1);
Func<double, double> E = (x) => x * norm.ProbabilityDensityFunction(x);
UFunction UE = (x) => x * norm.ProbabilityDensityFunction(x);
double expected = Quadpack.Integrate(UE,
Double.NegativeInfinity, Double.PositiveInfinity);
double actual = InfiniteAdaptiveGaussKronrod.Integrate(E,
Double.NegativeInfinity, Double.PositiveInfinity);
Assert.AreEqual(expected, actual, 1e-3);
Assert.AreEqual(norm.Mean, actual, 1e-3);
}
}
