public void icdf()
{
// install.packages('LaplacesDemon')
// library('LaplacesDemon')
//
BernoulliDistribution dist = new BernoulliDistribution(0.5);
double[] percentiles = Vector.Range(0.0, 1.0, stepSize: 0.1);
for (int i = 0; i < percentiles.Length; i++)
{
double x = percentiles[i];
int icdf = dist.InverseDistributionFunction(x);
double cdf = dist.DistributionFunction(icdf);
int iicdf = dist.InverseDistributionFunction(cdf);
double iiicdf = dist.DistributionFunction(iicdf);
if (i < 6) // qbern(p=((0:10)/10), prob=0.5)
{
Assert.AreEqual(0, icdf);
}
else
{
Assert.AreEqual(1, icdf);
}
double rx = System.Math.Round(x, MidpointRounding.ToEven);
double rc = System.Math.Round(cdf, MidpointRounding.ToEven);
Assert.AreEqual(rx, rc, 1e-5);
Assert.AreEqual(iicdf, icdf, 1e-5);
Assert.AreEqual(iiicdf, cdf, 1e-5);
}
}
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);
Assert.AreEqual(0, bern.Support.Min);
Assert.AreEqual(1, bern.Support.Max);
Assert.AreEqual(bern.InverseDistributionFunction(0), bern.Support.Min);
Assert.AreEqual(bern.InverseDistributionFunction(1), bern.Support.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 MedianTest()
{
{
// Special case for the Bernoulli distribution: while the median is 0.5,
// the inverse distribution function cannot return a double value and thus
// returns 1.
BernoulliDistribution target = new BernoulliDistribution(0.5);
int icdf = target.InverseDistributionFunction(0.5);
Assert.AreEqual(0, icdf);
Assert.AreEqual(0.5, target.Median);
// However, it should work if the Bernoulli is being used as a continuous distribution:
Assert.AreEqual(0.5, (target as IUnivariateDistribution).InverseDistributionFunction(0.5));
Assert.AreEqual(0.5, (target as IUnivariateDistribution <double>).InverseDistributionFunction(0.5));
}
{
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));
}
}
