public void MultinomialDistribution_Sum_FollowsMultinumialLaw()
{
var rand = new Random(0);
const int N = 42;
const int m = 4;
const int nubmerOfIterations = 10;
for (int i = 0; i < nubmerOfIterations; ++i)
{
double[] randomWeights = Enumerable.Range(0, m).Select(_ => rand.NextDouble()).ToArray();
double sum = 0.0;
for (int k1 = 0; k1 <= N; ++k1)
{
for (int k2 = 0; k1 + k2 <= N; ++k2)
{
for (int k3 = 0; k1 + k2 + k3 <= N; ++k3)
{
int k4 = N - k1 - k2 - k3;
sum += MultinomialDistribution.DensityAt(new[] { k1, k2, k3, k4 }, randomWeights);
}
}
}
Assert.Equal(1.0, sum, precision: 4);
}
}
public void MultinomialDistribution_OfSingleNumber_IsOne()
{
foreach (int i in new[] { 1, 2, 8, 42 })
{
var oneOfI = MultinomialDistribution.DensityAt(new int[] { i }, new double[] { 1.0 });
Assert.Equal(1, oneOfI);
}
}
public void MultinomialDistribution_WithNEqual1AndSameWeights_IsUniform()
{
foreach (int i in new[] { 1, 2, 8, 42 })
{
var density = Enumerable.Repeat(1.0, i);
for (int j = 0; j < i; ++j)
{
var dirac = Enumerable.Repeat(0, j).Concat(new[] { 1 }).Concat(Enumerable.Repeat(0, i - j - 1));
var allCertain = MultinomialDistribution.DensityAt(dirac, density);
Assert.Equal((double)1 / i, allCertain);
}
}
}
public void BinomialDistribution_WithCertainSingleOutcome_HasCertainCombinedOutcome()
{
foreach (int i in new[] { 1, 2, 8, 42 })
{
var allCertain = MultinomialDistribution.DensityAt(new int[] { i, 0 }, new double[] { 1.0, 0.0 });
Assert.Equal(1, allCertain);
}
foreach (int i in new[] { 1, 2, 8, 42 })
{
var allCertain = MultinomialDistribution.DensityAt(new int[] { i, 0, 0 }, new double[] { 1.0, 0.0, 0.0 });
Assert.Equal(1, allCertain);
}
}
