public void ProbabilityDensityFunctionTest()
{
int degreesOfFreedom;
double actual, expected, x;
ChiSquareDistribution target;
degreesOfFreedom = 1;
target = new ChiSquareDistribution(degreesOfFreedom);
x = 1;
actual = target.ProbabilityDensityFunction(x);
expected = 0.2420;
Assert.AreEqual(expected, actual, 1e-4);
degreesOfFreedom = 2;
target = new ChiSquareDistribution(degreesOfFreedom);
x = 2;
actual = target.ProbabilityDensityFunction(x);
expected = 0.1839;
Assert.AreEqual(expected, actual, 1e-4);
degreesOfFreedom = 10;
target = new ChiSquareDistribution(degreesOfFreedom);
x = 2;
actual = target.ProbabilityDensityFunction(x);
expected = 0.0077;
Assert.AreEqual(expected, actual, 1e-4);
}
public void ConstructorTest()
{
var chisq = new ChiSquareDistribution(degreesOfFreedom: 7);
double mean = chisq.Mean; // 7
double median = chisq.Median; // 6.345811195595612
double var = chisq.Variance; // 14
double cdf = chisq.DistributionFunction(x: 6.27); // 0.49139966433823956
double pdf = chisq.ProbabilityDensityFunction(x: 6.27); // 0.11388708001184455
double lpdf = chisq.LogProbabilityDensityFunction(x: 6.27); // -2.1725478476948092
double ccdf = chisq.ComplementaryDistributionFunction(x: 6.27); // 0.50860033566176044
double icdf = chisq.InverseDistributionFunction(p: cdf); // 6.2700000000852318
double hf = chisq.HazardFunction(x: 6.27); // 0.22392254197721179
double chf = chisq.CumulativeHazardFunction(x: 6.27); // 0.67609276602233315
string str = chisq.ToString(); // "χ²(x; df = 7)
Assert.AreEqual(7, mean);
Assert.AreEqual(6.345811195595612, median, 1e-6);
Assert.AreEqual(14, var);
Assert.AreEqual(0.67609276602233315, chf);
Assert.AreEqual(0.49139966433823956, cdf);
Assert.AreEqual(0.11388708001184455, pdf);
Assert.AreEqual(-2.1725478476948092, lpdf);
Assert.AreEqual(0.22392254197721179, hf);
Assert.AreEqual(0.50860033566176044, ccdf);
Assert.AreEqual(6.2700000000852318, icdf, 1e-6);
Assert.AreEqual("χ²(x; df = 7)", str);
}
/// <summary>
/// Constructs a Chi-Square Test.
/// </summary>
/// <param name="statistic">The test statistic.</param>
/// <param name="degreesOfFreedom">The chi-square distribution degrees of freedom.</param>
/// <param name="threshold">The significance threshold. By default, 0.05 will be used.</param>
///
public ChiSquareTest(double statistic, int degreesOfFreedom, double threshold)
{
this.Statistic = statistic;
this.Threshold = threshold;
this.distribution = new ChiSquareDistribution(degreesOfFreedom);
this.PValue = distribution.SurvivalFunction(Statistic);
}
public void ConstructorTest()
{
var chisq = new ChiSquareDistribution(degreesOfFreedom: 7);
double mean = chisq.Mean; // 7
double median = chisq.Median; // 6.345811195595612
double var = chisq.Variance; // 14
double mode = chisq.Mode; // 5.0
double cdf = chisq.DistributionFunction(x: 6.27); // 0.49139966433823956
double pdf = chisq.ProbabilityDensityFunction(x: 6.27); // 0.11388708001184455
double lpdf = chisq.LogProbabilityDensityFunction(x: 6.27); // -2.1725478476948092
double ccdf = chisq.ComplementaryDistributionFunction(x: 6.27); // 0.50860033566176044
double icdf = chisq.InverseDistributionFunction(p: cdf); // 6.2700000000852318
double hf = chisq.HazardFunction(x: 6.27); // 0.22392254197721179
double chf = chisq.CumulativeHazardFunction(x: 6.27); // 0.67609276602233315
string str = chisq.ToString(); // "χ²(x; df = 7)
Assert.AreEqual(7, mean);
Assert.AreEqual(6.345811195595612, median, 1e-6);
Assert.AreEqual(14, var);
Assert.AreEqual(5.0, mode);
Assert.AreEqual(0.67609276602233315, chf);
Assert.AreEqual(0.49139966433823956, cdf);
Assert.AreEqual(0.11388708001184455, pdf);
Assert.AreEqual(-2.1725478476948092, lpdf);
Assert.AreEqual(0.22392254197721179, hf);
Assert.AreEqual(0.50860033566176044, ccdf);
Assert.AreEqual(6.2700000000852318, icdf, 1e-6);
Assert.AreEqual("χ²(x; df = 7)", str);
var range1 = chisq.GetRange(0.95);
var range2 = chisq.GetRange(0.99);
var range3 = chisq.GetRange(0.01);
Assert.AreEqual(2.1673499092980579, range1.Min);
Assert.AreEqual(14.067140449340167, range1.Max);
Assert.AreEqual(1.2390423055679316, range2.Min);
Assert.AreEqual(18.475306906582361, range2.Max);
Assert.AreEqual(1.2390423055679316, range3.Min);
Assert.AreEqual(18.475306906582361, range3.Max);
}
public void DistributionFunctionTest()
{
int degreesOfFreedom;
double actual, expected, x;
ChiSquareDistribution target;
degreesOfFreedom = 1;
target = new ChiSquareDistribution(degreesOfFreedom);
x = 5;
actual = target.DistributionFunction(x);
expected = 0.9747;
Assert.AreEqual(expected, actual, 1e-4);
degreesOfFreedom = 5;
target = new ChiSquareDistribution(degreesOfFreedom);
x = 5;
actual = target.DistributionFunction(x);
expected = 0.5841;
Assert.AreEqual(expected, actual, 1e-4);
}
public void LogProbabilityDensityFunctionTest()
{
int degreesOfFreedom;
double actual, expected, x;
ChiSquareDistribution target;
degreesOfFreedom = 1;
target = new ChiSquareDistribution(degreesOfFreedom);
x = 1;
actual = target.LogProbabilityDensityFunction(x);
expected = System.Math.Log(target.ProbabilityDensityFunction(x));
Assert.AreEqual(expected, actual, 1e-10);
degreesOfFreedom = 2;
target = new ChiSquareDistribution(degreesOfFreedom);
x = 2;
actual = target.LogProbabilityDensityFunction(x);
expected = System.Math.Log(target.ProbabilityDensityFunction(x));
Assert.AreEqual(expected, actual, 1e-10);
degreesOfFreedom = 10;
target = new ChiSquareDistribution(degreesOfFreedom);
x = 2;
actual = target.LogProbabilityDensityFunction(x);
expected = System.Math.Log(target.ProbabilityDensityFunction(x));
Assert.AreEqual(expected, actual, 1e-10);
}
public void MedianTest()
{
var target = new ChiSquareDistribution(degreesOfFreedom: 4);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
/// <summary>
/// Construct a Chi-Square Test.
/// </summary>
/// <param name="expected">The expected variable values.</param>
/// <param name="observed">The observed variable values.</param>
/// <param name="degreesOfFreedom">The chi-square distribution degrees of freedom.</param>
/// <param name="threshold">The significance threshold. By default, 0.05 will be used.</param>
///
public ChiSquareTest(double[] expected, double[] observed, int degreesOfFreedom, double threshold)
{
if (expected == null)
throw new ArgumentNullException("expected");
if (observed == null)
throw new ArgumentNullException("observed");
// X² = sum(o - e)²
// -----
// e
double sum = 0.0;
for (int i = 0; i < observed.Length; i++)
{
double d = observed[i] - expected[i];
sum += (d * d) / expected[i];
}
this.Statistic = sum;
this.Threshold = threshold;
this.distribution = new ChiSquareDistribution(degreesOfFreedom);
this.PValue = distribution.SurvivalFunction(Statistic);
}
public void InverseCumulativeFunctionTest()
{
double a;
var target = new ChiSquareDistribution();
a = target.InverseDistributionFunction(0);
Assert.AreEqual(0.0, a, 1e-5);
Assert.IsFalse(double.IsNaN(a));
a = target.InverseDistributionFunction(1);
Assert.AreEqual(double.PositiveInfinity, a, 1e-5);
Assert.IsFalse(double.IsNaN(a));
}
public void ConstructorTest11()
{
var original = new ChiSquareDistribution(degreesOfFreedom: 7);
var chisq = GeneralContinuousDistribution.FromDensityFunction(
original.Support, original.ProbabilityDensityFunction);
for (double i = -10; i < +10; i += 0.1)
{
double expected = original.DistributionFunction(i);
double actual = chisq.DistributionFunction(i);
Assert.IsTrue(expected.IsRelativelyEqual(actual, 1e-5));
Assert.IsFalse(Double.IsNaN(actual));
Assert.IsFalse(Double.IsNaN(expected));
}
testChiSquare(chisq);
}
public void ConstructorTest10()
{
var original = new ChiSquareDistribution(degreesOfFreedom: 7);
var chisq = GeneralContinuousDistribution.FromDistributionFunction(
original.Support, original.DistributionFunction);
for (double i = -10; i < +10; i += 0.1)
{
double expected = original.ProbabilityDensityFunction(i);
double actual = chisq.ProbabilityDensityFunction(i);
double diff = Math.Abs(expected - actual);
Assert.AreEqual(expected, actual, 1e-8);
Assert.IsFalse(Double.IsNaN(actual));
Assert.IsFalse(Double.IsNaN(expected));
}
testChiSquare(chisq);
}
public void ConstructorTest11()
{
var original = new ChiSquareDistribution(degreesOfFreedom: 7);
var chisq = GeneralContinuousDistribution.FromDensityFunction(
original.Support, original.ProbabilityDensityFunction);
testChiSquare(chisq);
}