public void ProbabilityMassFunctionTest()
{
BernoulliDistribution target = new BernoulliDistribution(0.6);
double expected = 0.6;
double actual = target.ProbabilityMassFunction(1);
Assert.AreEqual(expected, actual, 1e-6);
}
public void ConstructorTest()
{
var bern = new BernoulliDistribution(mean: 0.42);
// Common measures
double mean = bern.Mean; // 0.42
double median = bern.Median; // 0.0
double var = bern.Variance; // 0.2436
double mode = bern.Mode; // 0.0
// Probability mass functions
double pdf = bern.ProbabilityMassFunction(k: 1); // 0.42
double lpdf = bern.LogProbabilityMassFunction(k: 0); // -0.54472717544167193
// Cumulative distribution function
double cdf = bern.DistributionFunction(k: 0); // 0.58
double ccdf = bern.ComplementaryDistributionFunction(k: 0); // 0.42
// Quantile function
int icdf0 = bern.InverseDistributionFunction(p: 0.57); // 0
int icdf1 = bern.InverseDistributionFunction(p: 0.59); // 1
double hf = bern.HazardFunction(x: 0); // 1.3809523809523814
double chf = bern.CumulativeHazardFunction(x: 0); // 0.86750056770472328
string str = bern.ToString(CultureInfo.InvariantCulture); // "Bernoulli(x; p = 0.42, q = 0.58)"
Assert.AreEqual(0.42, mean);
Assert.AreEqual(0.0, median);
Assert.AreEqual(0.2436, var);
Assert.AreEqual(0.0, mode);
Assert.AreEqual(0.86750056770472328, chf, 1e-10);
Assert.AreEqual(0.58, cdf, 1e-10);
Assert.AreEqual(0.42, pdf);
Assert.AreEqual(-0.54472717544167193, lpdf);
Assert.AreEqual(1.3809523809523814, hf, 1e-10);
Assert.AreEqual(0.42, ccdf, 1e-10);
Assert.AreEqual(0, icdf0);
Assert.AreEqual(1, icdf1);
Assert.AreEqual("Bernoulli(x; p = 0.42, q = 0.58)", str);
var range1 = bern.GetRange(0.95);
var range2 = bern.GetRange(0.99);
var range3 = bern.GetRange(0.01);
Assert.AreEqual(0, range1.Min);
Assert.AreEqual(1.0, range1.Max);
Assert.AreEqual(0, range2.Min);
Assert.AreEqual(1.0, range2.Max);
Assert.AreEqual(0, range3.Min);
Assert.AreEqual(1.0, range3.Max);
}
public void MedianTest()
{
{
BernoulliDistribution target = new BernoulliDistribution(0.2);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
{
BernoulliDistribution target = new BernoulliDistribution(0.6);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
{
BernoulliDistribution target = new BernoulliDistribution(0.0);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
{
BernoulliDistribution target = new BernoulliDistribution(1.0);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
}
public void ComplementaryDistributionFunctionTest()
{
BernoulliDistribution target = new BernoulliDistribution(0.42);
{
double expected = 1.0 - target.DistributionFunction(0);
double actual = target.ComplementaryDistributionFunction(0);
Assert.AreEqual(expected, actual, 1e-6);
}
{
double expected = 1.0 - target.DistributionFunction(1);
double actual = target.ComplementaryDistributionFunction(1);
Assert.AreEqual(expected, actual, 1e-6);
}
{
double expected = 1.0 - target.DistributionFunction(-1);
double actual = target.ComplementaryDistributionFunction(-1);
Assert.AreEqual(expected, actual, 1e-6);
}
{
double expected = 1.0 - target.DistributionFunction(2);
double actual = target.ComplementaryDistributionFunction(2);
Assert.AreEqual(expected, actual, 1e-6);
}
}
public void DistributionFunctionTest()
{
BernoulliDistribution target = new BernoulliDistribution(0.6);
double expected = 0.4;
double actual = target.DistributionFunction(0);
Assert.AreEqual(expected, actual, 1e-6);
}
public void GenerationTest()
{
double prob = 0.5;
int trials = 10000;
BernoulliDistribution target = new BernoulliDistribution(prob);
target.Fit(target.Generate(trials).Select(x => (double)x).ToArray());
Assert.AreEqual(target.Mean, prob, 0.01);
}