PoissonDistribution Class

[SerializableAttribute]
public class PoissonDistribution : DiscreteDistribution

<SerializableAttribute>
Public Class PoissonDistribution
	Inherits DiscreteDistribution

[SerializableAttribute]
public ref class PoissonDistribution : public DiscreteDistribution

[<SerializableAttribute>]
type PoissonDistribution =  
    class
        inherit DiscreteDistribution
    end

The PoissonDistribution type exposes the following members.

	Name	Description
	PoissonDistribution(Double)	Constructs a new PoissonDistribution.
	PoissonDistribution(VectorDouble)	Estimates the parameters of the distribution of a variable assuming it follows a Poisson distribution.

	Name	Description
	Entropy	Gets the entropy of the distribution. (Overrides DistributionEntropy.)
	IsUnimodal	Gets whether the distribution has one or more modes. (Inherited from DiscreteDistribution.)
	Kurtosis	Gets the kurtosis of the distribution. (Overrides DistributionKurtosis.)
	Mean	Gets the mean or expectation value of the distribution. (Overrides DistributionMean.)
	Mode	Gets the mode of the distribution. (Overrides DiscreteDistributionMode.)
	NumberOfModes	Gets the number of modes of the distribution. (Overrides DiscreteDistributionNumberOfModes.)
	Skewness	Gets the skewness of the distribution. (Overrides DistributionSkewness.)
	StandardDeviation	Gets the standard deviation of the distribution. (Inherited from Distribution.)
	StatisticSymbol	Gets the common symbol to describe a statistic from the distribution. (Inherited from Distribution.)
	Variance	Gets the variance of the distribution. (Overrides DistributionVariance.)

	Name	Description
	DistributionFunction	Evaluates the cumulative distribution function of the distribution. (Overrides DiscreteDistributionDistributionFunction(Int32).)
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetAllModes	Returns an array that contains all the modes of the distribution. (Overrides DiscreteDistributionGetAllModes.)
	GetExpectedHistogram(IndexIntervalInt32, Double)	Returns a histogram whose bins contain the expected number of samples from the distribution for a given total number of samples. (Inherited from DiscreteDistribution.)
	GetExpectedHistogram(IndexInt32, Double)	Returns a histogram whose bins contain the expected number of samples from the distribution for a given total number of samples. (Inherited from DiscreteDistribution.)
	GetExpectedHistogram(Int32, Int32, Double)	Returns a histogram whose bins contain the expected number of samples from the distribution for a given total number of samples. (Inherited from DiscreteDistribution.)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetRandomSequence	Returns a sequence of random samples from the distribution. (Inherited from DiscreteDistribution.)
	GetRandomSequence(Random)	Returns a sequence of random samples from the distribution. (Inherited from DiscreteDistribution.)
	GetRandomSequence(Random, Int32)	Returns a sequence of random samples of the specified length from the distribution. (Inherited from DiscreteDistribution.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	InverseDistributionFunction	Returns the inverse of the distribution function. (Inherited from DiscreteDistribution.)
	LeftTailProbability	Gets the probability of obtaining a sample that is less than or less than or equal to the specified upper bound. (Inherited from DiscreteDistribution.)
	LogProbability	Returns the logarithm of the probability of obtaining a specific integer value in the distribution. (Overrides DiscreteDistributionLogProbability(Int32).)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	Probability(Int32)	Evaluates the probability function of the distribution. (Overrides DiscreteDistributionProbability(Int32).)
	Probability(Int32, Int32)	Gets the probability of obtaining a sample that falls within the specified interval from the distribution. (Inherited from DiscreteDistribution.)
	RightTailProbability	Gets the probability of obtaining a sample that is less than or less than or equal to the specified upper bound. (Inherited from DiscreteDistribution.)
	Sample	Returns a random sample from the distribution. (Inherited from DiscreteDistribution.)
	Sample(Int32)	Returns a vector of random samples from the distribution. (Inherited from DiscreteDistribution.)
	Sample(Random)	Returns a random sample from the distribution. (Overrides DiscreteDistributionSample(Random).)
	Sample(Int32, Random)	Returns a vector of random samples from the distribution. (Inherited from DiscreteDistribution.)
	Sample(Random, Int32)	Fills an Int32 array with random numbers. (Inherited from DiscreteDistribution.)
	Sample(Random, Double)	Gets a single sample from the Poisson distribution with the specified mean.
	Sample(Random, Int32, Int32, Int32)	Fills an Int32 array with random numbers from this DiscreteDistribution. (Inherited from DiscreteDistribution.)
	ToString	Returns a string that represents the current object. (Overrides ObjectToString.)
	TwoTailProbability	Gets the probability of obtaining a sample that is less than or less than or equal to the specified upper bound. (Inherited from DiscreteDistribution.)

The Poisson distribution models the number of occurrances of an event where each event has a constant probability of occurring. It is closely related to the exponential distribution, which models the time between successive occurrances.

The Poisson distribution has one parameter: the mean number of occurrances per unit time.

The number of failures of a piece of equipment that is replaced with identical copies when it fails follows a Poisson distribution.

Reference