public void FitTest2()
{
int[] symbols = { 3, 5 };
JointDistribution target = new JointDistribution(symbols);
double[][] observations =
{
new double[] { 0, 0 },
new double[] { 1, 1 },
new double[] { 2, 1 },
};
double[] weights = { 2, 1, 1 };
target.Fit(observations, weights);
double[] p = target.Frequencies;
double actual;
actual = target.ProbabilityMassFunction(new[] { 0, 0 });
Assert.AreEqual(0.5, actual);
actual = target.ProbabilityMassFunction(new[] { 1, 1 });
Assert.AreEqual(0.25, actual);
actual = target.ProbabilityMassFunction(new[] { 2, 1 });
Assert.AreEqual(0.25, actual);
}
public void JointDistributionConstructorTest()
{
int[] symbols = { 3, 5 };
JointDistribution target = new JointDistribution(symbols);
double[] p = target.Frequencies;
Assert.AreEqual(3 * 5, p.Length);
for (int i = 0; i < p.Length; i++)
{
p[i] = i;
}
double actual;
actual = target.ProbabilityMassFunction(new int[] { 0, 0 });
Assert.AreEqual(0, actual);
actual = target.ProbabilityMassFunction(new int[] { 0, 1 });
Assert.AreEqual(1, actual);
actual = target.ProbabilityMassFunction(new int[] { 1, 0 });
Assert.AreEqual(5, actual);
actual = target.ProbabilityMassFunction(new int[] { 2, 4 });
Assert.AreEqual(14, actual);
}
public void UniformTest()
{
int a = 2;
int b = 5;
int n = b - a + 1;
// Wikipedia definitions
double expectedMean = (a + b) / 2.0;
double expectedVar = (System.Math.Pow(b - a + 1, 2) - 1) / 12.0;
double p = 1.0 / n;
JointDistribution dist = JointDistribution.Uniform(1, a, b);
Assert.AreEqual(expectedMean, dist.Mean[0]);
// Assert.AreEqual(expectedVar, dist.Variance);
Assert.AreEqual(n, dist.Frequencies.Length);
Assert.AreEqual(0, dist.ProbabilityMassFunction(new[] { 0 }));
Assert.AreEqual(0, dist.ProbabilityMassFunction(new[] { 1 }));
Assert.AreEqual(p, dist.ProbabilityMassFunction(new[] { 2 }));
Assert.AreEqual(p, dist.ProbabilityMassFunction(new[] { 3 }));
Assert.AreEqual(p, dist.ProbabilityMassFunction(new[] { 4 }));
Assert.AreEqual(p, dist.ProbabilityMassFunction(new[] { 5 }));
Assert.AreEqual(0, dist.ProbabilityMassFunction(new[] { 6 }));
Assert.AreEqual(0, dist.ProbabilityMassFunction(new[] { 7 }));
}
public void MeanTest3()
{
var target = new JointDistribution(new[] { 2 }, new [] { 0.5, 0.5 });
double expected = (2.0 + 3.0) / 2.0;
double actual = target.Mean[0];
Assert.AreEqual(expected, actual);
}
public void MeanTest2()
{
var target = new JointDistribution(new [] { 42 }, new[] { 0.1, 0.4, 0.5 });
double expected = 42 * 0.1 + 43 * 0.4 + 44 * 0.5;
double actual = target.Mean[0];
Assert.AreEqual(expected, actual);
}
public void ProbabilityMassFunctionTest()
{
JointDistribution dist = JointDistribution.Uniform(1, 2, 5);
double p = 0.25;
Assert.AreEqual(0, dist.ProbabilityMassFunction(new[] { 0 }));
Assert.AreEqual(0, dist.ProbabilityMassFunction(new[] { 1 }));
Assert.AreEqual(p, dist.ProbabilityMassFunction(new[] { 2 }));
Assert.AreEqual(p, dist.ProbabilityMassFunction(new[] { 3 }));
Assert.AreEqual(p, dist.ProbabilityMassFunction(new[] { 4 }));
Assert.AreEqual(p, dist.ProbabilityMassFunction(new[] { 5 }));
Assert.AreEqual(0, dist.ProbabilityMassFunction(new[] { 6 }));
Assert.AreEqual(0, dist.ProbabilityMassFunction(new[] { 7 }));
}
public void FitTest_vector_inputs()
{
double[] expected = { 0.50, 0.00, 0.25, 0.25 };
JointDistribution target;
double[] values = { 0.00, 2.00, 3.00 };
double[] weights = { 0.50, 0.25, 0.25 };
target = new JointDistribution(new[] { 4 });
target.Fit(Jagged.ColumnVector(values), weights);
double[] actual = target.Frequencies;
Assert.IsTrue(Matrix.IsEqual(expected, actual));
}
public void FitTest3()
{
JointDistribution target = new JointDistribution(new[] { -1 }, new[] { 4 });
double[] values = { 0.00, 1.00, 2.00, 3.00 };
double[] weights = { 0.25, 0.25, 0.25, 0.25 };
target.Fit(Jagged.ColumnVector(values).Subtract(1), weights);
double[] expected = { 0.25, 0.25, 0.25, 0.25 };
double[] actual = target.Frequencies;
Assert.IsTrue(Matrix.IsEqual(expected, actual));
}
public void LogProbabilityMassFunctionTest()
{
JointDistribution dist = JointDistribution.Uniform(1, 2, 5);
double p = System.Math.Log(0.25);
double l = System.Math.Log(0);
Assert.AreEqual(l, dist.LogProbabilityMassFunction(new[] { 0 }));
Assert.AreEqual(l, dist.LogProbabilityMassFunction(new[] { 1 }));
Assert.AreEqual(p, dist.LogProbabilityMassFunction(new[] { 2 }));
Assert.AreEqual(p, dist.LogProbabilityMassFunction(new[] { 3 }));
Assert.AreEqual(p, dist.LogProbabilityMassFunction(new[] { 4 }));
Assert.AreEqual(p, dist.LogProbabilityMassFunction(new[] { 5 }));
Assert.AreEqual(l, dist.LogProbabilityMassFunction(new[] { 6 }));
Assert.AreEqual(l, dist.LogProbabilityMassFunction(new[] { 7 }));
}
public void DistributionFunctionTest()
{
var target = new JointDistribution(new[] { 0.1, 0.4, 0.5 });
double actual;
actual = target.DistributionFunction(new[] { 0 });
Assert.AreEqual(0.1, actual, 1e-6);
actual = target.DistributionFunction(new[] { 1 });
Assert.AreEqual(0.5, actual, 1e-6);
actual = target.DistributionFunction(new[] { 2 });
Assert.AreEqual(1.0, actual, 1e-6);
actual = target.DistributionFunction(new[] { 3 });
Assert.AreEqual(1.0, actual, 1e-6);
}
public void MarginalTest()
{
// Example from https://en.wikipedia.org/wiki/Marginal_distribution
int[][] data =
{
new[] { 4, 2, 1, 1 },
new[] { 2, 4, 1, 1 },
new[] { 2, 2, 2, 2 },
new[] { 8, 0, 0, 0 },
};
double[][] frequencies = data.Divide(32);
var joint = new JointDistribution(frequencies.ToMatrix());
double[] x = joint.MarginalDistributionFunction(0);
double[] y = joint.MarginalDistributionFunction(1);
double[][] expected =
{
new[] { 16 / 32.0, 8 / 32.0, 4 / 32.0, 4 / 32.0 },
new[] { 8 / 32.0, 8 / 32.0, 8 / 32.0, 8 / 32.0 }
};
Assert.IsTrue(x.IsEqual(expected[0]));
Assert.IsTrue(y.IsEqual(expected[1]));
for (int i = 0; i < 4; i++)
{
double a = joint.MarginalDistributionFunction(0, i);
Assert.AreEqual(a, expected[0][i]);
}
for (int i = 0; i < 4; i++)
{
double a = joint.MarginalDistributionFunction(1, i);
Assert.AreEqual(a, expected[1][i]);
}
}
