public void ConstructorTest()
{
// Create a new Poisson distribution with
var dist = new PoissonDistribution(lambda: 4.2);
// Common measures
double mean = dist.Mean; // 4.2
double median = dist.Median; // 4.0
double var = dist.Variance; // 4.2
// Cumulative distribution functions
double cdf = dist.DistributionFunction(k: 2); // 0.39488100648845126
double ccdf = dist.ComplementaryDistributionFunction(k: 2); // 0.60511899351154874
// Probability mass functions
double pmf1 = dist.ProbabilityMassFunction(k: 4); // 0.19442365170822165
double pmf2 = dist.ProbabilityMassFunction(k: 5); // 0.1633158674349062
double pmf3 = dist.ProbabilityMassFunction(k: 6); // 0.11432110720443435
double lpmf = dist.LogProbabilityMassFunction(k: 2); // -2.0229781299813
// 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); // 7
// Hazard (failure rate) functions
double hf = dist.HazardFunction(x: 4); // 0.19780423301883465
double chf = dist.CumulativeHazardFunction(x: 4); // 0.017238269667812049
// String representation
string str = dist.ToString(CultureInfo.InvariantCulture); // "Poisson(x; λ = 4.2)"
// Median bounds
// (http://en.wikipedia.org/wiki/Poisson_distribution#Median)
Assert.IsTrue(median < 4.2 + 1 / 3.0);
Assert.IsTrue(4.2 - System.Math.Log(2) <= median);
Assert.AreEqual(4.2, mean);
Assert.AreEqual(4.0, median);
Assert.AreEqual(4.2, var);
Assert.AreEqual(0.017238269667812049, chf, 1e-10);
Assert.AreEqual(0.39488100648845126, cdf);
Assert.AreEqual(0.19442365170822165, pmf1);
Assert.AreEqual(0.1633158674349062, pmf2);
Assert.AreEqual(0.11432110720443435, pmf3);
Assert.AreEqual(-2.0229781299813, lpmf);
Assert.AreEqual(0.19780423301883465, hf);
Assert.AreEqual(0.60511899351154874, ccdf);
Assert.AreEqual(2, icdf1);
Assert.AreEqual(4, icdf2);
Assert.AreEqual(7, icdf3);
Assert.AreEqual("Poisson(x; λ = 4.2)", str);
}
