public void ConstructorTest()
{
// Create a Negative Binomial distribution with r = 7, p = 0.42
var dist = new NegativeBinomialDistribution(failures: 7, probability: 0.42);
// Common measures
double mean = dist.Mean; // 5.068965517241379
double median = dist.Median; // 5.0
double var = dist.Variance; // 8.7395957193816862
// Cumulative distribution functions
double cdf = dist.DistributionFunction(k: 2); // 0.19605133020527743
double ccdf = dist.ComplementaryDistributionFunction(k: 2); // 0.80394866979472257
// Probability mass functions
double pmf1 = dist.ProbabilityMassFunction(k: 4); // 0.054786846293416853
double pmf2 = dist.ProbabilityMassFunction(k: 5); // 0.069908015870399909
double pmf3 = dist.ProbabilityMassFunction(k: 6); // 0.0810932984096639
double lpmf = dist.LogProbabilityMassFunction(k: 2); // -2.3927801721315989
// Quantile function
int icdf1 = dist.InverseDistributionFunction(p: 0.17); // 2
int icdf2 = dist.InverseDistributionFunction(p: 0.46); // 4
int icdf3 = dist.InverseDistributionFunction(p: 0.87); // 8
// Hazard (failure rate) functions
double hf = dist.HazardFunction(x: 4); // 0.10490438293398294
double chf = dist.CumulativeHazardFunction(x: 4); // 0.64959916255036043
// String representation
string str = dist.ToString(CultureInfo.InvariantCulture); // "NegativeBinomial(x; r = 7, p = 0.42)"
Assert.AreEqual(5.068965517241379, mean);
Assert.AreEqual(5.0, median);
Assert.AreEqual(8.7395957193816862, var);
Assert.AreEqual(0.64959916255036043, chf, 1e-10);
Assert.AreEqual(0.19605133020527743, cdf);
Assert.AreEqual(0.054786846293416853, pmf1);
Assert.AreEqual(0.069908015870399909, pmf2);
Assert.AreEqual(0.0810932984096639, pmf3);
Assert.AreEqual(-3.8297538146412009, lpmf);
Assert.AreEqual(0.10490438293398294, hf);
Assert.AreEqual(0.80394866979472257, ccdf);
Assert.AreEqual(2, icdf1);
Assert.AreEqual(4, icdf2);
Assert.AreEqual(8, icdf3);
Assert.AreEqual("NegativeBinomial(x; r = 7, p = 0.42)", str);
var range1 = dist.GetRange(0.95);
var range2 = dist.GetRange(0.99);
var range3 = dist.GetRange(0.01);
Assert.AreEqual(1, range1.Min);
Assert.AreEqual(11.0, range1.Max);
Assert.AreEqual(0, range2.Min);
Assert.AreEqual(14, range2.Max);
Assert.AreEqual(0, range3.Min);
Assert.AreEqual(14, range3.Max);
}
public void MedianTest()
{
for (int i = 0; i < 10; i++)
{
int failures = i + 1;
{
var target = new NegativeBinomialDistribution(failures, 0.0);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
{
var target = new NegativeBinomialDistribution(failures, 0.7);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
{
var target = new NegativeBinomialDistribution(failures, 0.2);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
{
var target = new NegativeBinomialDistribution(failures, 1.0);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
}
}
public void icdf2()
{
int trials = 1;
var dist = new NegativeBinomialDistribution(trials, 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);
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()
{
#region doc_example
// Create a Negative Binomial distribution with r = 7, p = 0.42
var dist = new NegativeBinomialDistribution(failures: 7, probability: 0.42);
// Common measures
double mean = dist.Mean; // 5.068965517241379
double median = dist.Median; // 9.0
double var = dist.Variance; // 8.7395957193816862
// Cumulative distribution functions
double cdf = dist.DistributionFunction(k: 2); // 0.033380251139644379
double ccdf = dist.ComplementaryDistributionFunction(k: 2); // 0.96661974886035562
// Probability mass functions
double pmf1 = dist.ProbabilityMassFunction(k: 4); // 0.054786846293416853
double pmf2 = dist.ProbabilityMassFunction(k: 5); // 0.069908015870399909
double pmf3 = dist.ProbabilityMassFunction(k: 6); // 0.0810932984096639
double lpmf = dist.LogProbabilityMassFunction(k: 2); // -2.3927801721315989
// Quantile function
int icdf = dist.InverseDistributionFunction(p: cdf); // 2
int icdf1 = dist.InverseDistributionFunction(p: 0.17); // 5
int icdf2 = dist.InverseDistributionFunction(p: 0.46); // 9
int icdf3 = dist.InverseDistributionFunction(p: 0.87); // 15
// Hazard (failure rate) functions
double hf = dist.HazardFunction(x: 4); // 0.062681673912893129
double chf = dist.CumulativeHazardFunction(x: 4); // 0.13461898882526471
// String representation
string str = dist.ToString(CultureInfo.InvariantCulture); // "NegativeBinomial(x; r = 7, p = 0.42)"
#endregion
double[] probabilities = new double[10];
for (int i = 0; i < probabilities.Length; i++)
{
probabilities[i] = dist.DistributionFunction(i);
}
Assert.AreEqual(5.068965517241379, mean);
Assert.AreEqual(9.0, median);
Assert.AreEqual(8.7395957193816862, var);
Assert.AreEqual(0.13461898882526471, chf, 1e-10);
Assert.AreEqual(0.033380251139644379, cdf);
Assert.AreEqual(0.054786846293416853, pmf1);
Assert.AreEqual(0.069908015870399909, pmf2);
Assert.AreEqual(0.0810932984096639, pmf3);
Assert.AreEqual(-3.8297538146412009, lpmf);
Assert.AreEqual(0.062681673912893129, hf);
Assert.AreEqual(0.96661974886035562, ccdf);
Assert.AreEqual(2, icdf);
Assert.AreEqual(5, icdf1);
Assert.AreEqual(9, icdf2);
Assert.AreEqual(15, icdf3);
Assert.AreEqual("NegativeBinomial(x; r = 7, p = 0.42)", str);
var range1 = dist.GetRange(0.95);
var range2 = dist.GetRange(0.99);
var range3 = dist.GetRange(0.01);
Assert.AreEqual(3, range1.Min);
Assert.AreEqual(18.0, range1.Max);
Assert.AreEqual(1, range2.Min);
Assert.AreEqual(23, range2.Max);
Assert.AreEqual(1, range3.Min);
Assert.AreEqual(23, range3.Max);
}