public void ConstructorTest()
{
// Create a new mixture containing two Normal distributions
Mixture <NormalDistribution> mix = new Mixture <NormalDistribution>(
new NormalDistribution(2, 1), new NormalDistribution(5, 1));
// Common measures
double mean = mix.Mean; // 3.5
double median = mix.Median; // 3.4999998506015895
double var = mix.Variance; // 3.25
// Cumulative distribution functions
double cdf = mix.DistributionFunction(x: 4.2); // 0.59897597553494908
double ccdf = mix.ComplementaryDistributionFunction(x: 4.2); // 0.40102402446505092
// Probability mass functions
double pmf1 = mix.ProbabilityDensityFunction(x: 1.2); // 0.14499174984363708
double pmf2 = mix.ProbabilityDensityFunction(x: 2.3); // 0.19590437513747333
double pmf3 = mix.ProbabilityDensityFunction(x: 3.7); // 0.13270883471234715
double lpmf = mix.LogProbabilityDensityFunction(x: 4.2); // -1.8165661905848629
// Quantile function
double icdf1 = mix.InverseDistributionFunction(p: 0.17); // 1.5866611690305095
double icdf2 = mix.InverseDistributionFunction(p: 0.46); // 3.1968506765456883
double icdf3 = mix.InverseDistributionFunction(p: 0.87); // 5.6437596300843076
// Hazard (failure rate) functions
double hf = mix.HazardFunction(x: 4.2); // 0.40541978256972522
double chf = mix.CumulativeHazardFunction(x: 4.2); // 0.91373394208601633
// String representation:
// Mixture(x; 0.5 * N(x; μ = 5, σ² = 1) + 0.5 * N(x; μ = 5, σ² = 1))
string str = mix.ToString(CultureInfo.InvariantCulture);
Assert.AreEqual(3.5, mean);
Assert.AreEqual(3.4999998506015895, median);
Assert.AreEqual(3.25, var);
Assert.AreEqual(0.91373394208601633, chf, 1e-10);
Assert.AreEqual(0.59897597553494908, cdf);
Assert.AreEqual(0.14499174984363708, pmf1);
Assert.AreEqual(0.19590437513747333, pmf2);
Assert.AreEqual(0.13270883471234715, pmf3);
Assert.AreEqual(-1.8165661905848629, lpmf);
Assert.AreEqual(0.40541978256972522, hf);
Assert.AreEqual(0.40102402446505092, ccdf);
Assert.AreEqual(1.5866611690305092, icdf1);
Assert.AreEqual(3.1968506765456883, icdf2);
Assert.AreEqual(5.6437596300843076, icdf3);
Assert.AreEqual("Mixture(x; 0.5*N(x; μ = 5, σ² = 1) + 0.5*N(x; μ = 5, σ² = 1))", str);
Assert.IsFalse(double.IsNaN(icdf1));
}
public void ConstructorTest()
{
// Create a new mixture containing two Normal distributions
Mixture<NormalDistribution> mix = new Mixture<NormalDistribution>(
new NormalDistribution(2, 1), new NormalDistribution(5, 1));
// Common measures
double mean = mix.Mean; // 3.5
double median = mix.Median; // 3.4999998506015895
double var = mix.Variance; // 3.25
// Cumulative distribution functions
double cdf = mix.DistributionFunction(x: 4.2); // 0.59897597553494908
double ccdf = mix.ComplementaryDistributionFunction(x: 4.2); // 0.40102402446505092
// Probability mass functions
double pmf1 = mix.ProbabilityDensityFunction(x: 1.2); // 0.14499174984363708
double pmf2 = mix.ProbabilityDensityFunction(x: 2.3); // 0.19590437513747333
double pmf3 = mix.ProbabilityDensityFunction(x: 3.7); // 0.13270883471234715
double lpmf = mix.LogProbabilityDensityFunction(x: 4.2); // -1.8165661905848629
// Quantile function
double icdf1 = mix.InverseDistributionFunction(p: 0.17); // 1.5866611690305095
double icdf2 = mix.InverseDistributionFunction(p: 0.46); // 3.1968506765456883
double icdf3 = mix.InverseDistributionFunction(p: 0.87); // 5.6437596300843076
// Hazard (failure rate) functions
double hf = mix.HazardFunction(x: 4.2); // 0.40541978256972522
double chf = mix.CumulativeHazardFunction(x: 4.2); // 0.91373394208601633
// String representation:
// Mixture(x; 0.5 * N(x; μ = 5, σ² = 1) + 0.5 * N(x; μ = 5, σ² = 1))
string str = mix.ToString(CultureInfo.InvariantCulture);
Assert.AreEqual(3.5, mean);
Assert.AreEqual(3.4999998506015895, median);
Assert.AreEqual(3.25, var);
Assert.AreEqual(0.91373394208601633, chf, 1e-10);
Assert.AreEqual(0.59897597553494908, cdf);
Assert.AreEqual(0.14499174984363708, pmf1);
Assert.AreEqual(0.19590437513747333, pmf2);
Assert.AreEqual(0.13270883471234715, pmf3);
Assert.AreEqual(-1.8165661905848629, lpmf);
Assert.AreEqual(0.40541978256972522, hf);
Assert.AreEqual(0.40102402446505092, ccdf);
Assert.AreEqual(1.5866611690305095, icdf1);
Assert.AreEqual(3.1968506765456883, icdf2);
Assert.AreEqual(5.6437596300843076, icdf3);
Assert.AreEqual("Mixture(x; 0.5*N(x; μ = 5, σ² = 1) + 0.5*N(x; μ = 5, σ² = 1))", str);
}
public void ProbabilityDensityFunctionPerComponent()
{
NormalDistribution[] components = new NormalDistribution[2];
components[0] = new NormalDistribution(2, 1);
components[1] = new NormalDistribution(5, 1);
double[] coefficients = { 0.4, 0.5 };
var mixture = new Mixture <NormalDistribution>(coefficients, components);
double expected = mixture.ProbabilityDensityFunction(0, 0.42) +
mixture.ProbabilityDensityFunction(1, 0.42);
double actual = mixture.ProbabilityDensityFunction(0.42);
Assert.AreEqual(expected, actual);
}
/// <summary>
/// Returns the most likely clusters of an observation.
/// </summary>
/// <param name="observation">An input observation.</param>
/// <returns>
/// The index of the most likely cluster
/// of the given observation. </returns>
public int Classify(double[] observation)
{
if (observation == null)
{
throw new ArgumentNullException("observation");
}
int imax = 0;
double max = model.ProbabilityDensityFunction(0, observation);
for (int i = 1; i < model.Components.Length; i++)
{
double p = model.ProbabilityDensityFunction(i, observation);
if (p > max)
{
max = p;
imax = i;
}
}
return(imax);
}
public void ProbabilityDensityFunction()
{
NormalDistribution[] components = new NormalDistribution[2];
components[0] = new NormalDistribution(2, 1);
components[1] = new NormalDistribution(5, 1);
double[] coefficients = { 0.4, 0.5 };
var mixture = new Mixture<NormalDistribution>(coefficients, components);
double expected = 0.4 * components[0].ProbabilityDensityFunction(0.42) +
0.5 * components[1].ProbabilityDensityFunction(0.42);
double actual = mixture.ProbabilityDensityFunction(0.42);
Assert.AreEqual(expected, actual);
}