PoissonDistribution Class

[SerializableAttribute]
public class PoissonDistribution : UnivariateDiscreteDistribution, 
	IFittableDistribution<double, IFittingOptions>, IFittable<double, IFittingOptions>, 
	IFittable<double>, IFittableDistribution<double>, IDistribution<double>, 
	IDistribution, ICloneable, ISampleableDistribution<int>, IDistribution<int>, 
	IRandomNumberGenerator<int>

<SerializableAttribute>
Public Class PoissonDistribution
	Inherits UnivariateDiscreteDistribution
	Implements IFittableDistribution(Of Double, IFittingOptions), 
	IFittable(Of Double, IFittingOptions), IFittable(Of Double), 
	IFittableDistribution(Of Double), IDistribution(Of Double), IDistribution, 
	ICloneable, ISampleableDistribution(Of Integer), IDistribution(Of Integer), 
	IRandomNumberGenerator(Of Integer)

// 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 cdf1 = dist.DistributionFunction(k: 2); // 0.21023798702309743
double cdf2 = dist.DistributionFunction(k: 4); // 0.58982702131057763
double cdf3 = dist.DistributionFunction(k: 7); // 0.93605666027257894
double ccdf = dist.ComplementaryDistributionFunction(k: 2); // 0.78976201297690252

// 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: cdf1); // 2
int icdf2 = dist.InverseDistributionFunction(p: cdf2); // 4
int icdf3 = dist.InverseDistributionFunction(p: cdf3); // 7

// Hazard (failure rate) functions
double hf = dist.HazardFunction(x: 4); // 0.47400404660843515
double chf = dist.CumulativeHazardFunction(x: 4); // 0.89117630901575073

// String representation
string str = dist.ToString(CultureInfo.InvariantCulture); // "Poisson(x; λ = 4.2)"

// Create a new Poisson distribution
var dist = new PoissonDistribution(lambda: 4.2);

// P(X = 1) = 0.0629814226460064
double equal = dist.ProbabilityMassFunction(k: 1);

// P(X < 1) = 0.0149955768204777
double less = dist.DistributionFunction(k: 1, inclusive: false);

// P(X ≤ 1) = 0.0779769994664841
double lessThanOrEqual = dist.DistributionFunction(k: 1, inclusive: true);

// P(X > 1) = 0.922023000533516
double greater = dist.ComplementaryDistributionFunction(k: 1);

// P(X ≥ 1) = 0.985004423179522
double greaterThanOrEqual = dist.ComplementaryDistributionFunction(k: 1, inclusive: true);