﻿PoissonDistribution Class

# PoissonDistribution Class

Class PoissonDistribution represents a poisson distribution with a specified lambda, which is both the mean and the variance of the distribution. The poisson distribution a discrete distribution representing the probability of obtaining exactly n successes in N trials.
Inheritance Hierarchy

Namespace:  CenterSpace.NMath.Core
Assembly:  NMath (in NMath.dll) Version: 7.4
Syntax
```[SerializableAttribute]
public class PoissonDistribution : ProbabilityDistribution,
IRandomVariableMoments```

The PoissonDistribution type exposes the following members.

Constructors
NameDescription
PoissonDistribution
Constructs a PoissonDistribution with the specified lambda, which is both the mean and the variance of the distribution.
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Properties
NameDescription
Kurtosis
Gets the kurtosis, a measure of the degree of peakednesss of the distribution.
Mean
Gets and sets the mean of the distribution.
Skewness
Gets the skewness, a measure of the degree of asymmetry of this distribution.
Variance
Gets and sets the variance of the distribution.
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Methods
NameDescription
CDF
Returns the cumulative distribution function evaluated at a given value.
(Overrides ProbabilityDistributionCDF(Double).)
Clone
Creates a deep copy of this PoissonDistribution.
(Overrides ProbabilityDistributionClone.)
InverseCDF
Returns the inverse cumulative distribution function evaluated at a given value.
(Overrides ProbabilityDistributionInverseCDF(Double).)
InverseCdfUsingBracket
Uses a bracketing method to evaluate the inverse of cumulative distribution functions.
(Inherited from ProbabilityDistribution.)
InverseDiscreteCdfUsingBracket
Uses a bracketing method to evaluate the inverse of cumulative distribution functions for discrete distributions.
(Inherited from ProbabilityDistribution.)
PDF
Returns the probability density function evaluated at a given value.
(Overrides ProbabilityDistributionPDF(Double).)
ToString
Returns a formatted string representation of this distribution.
(Overrides ProbabilityDistributionToString.)
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Remarks
The Poisson Distribution is often used as a model for the number of events in a specific time period. The distribution function for the Poisson distribution is:
`f(x) = exp(-1*lambda) lambda^x / x!`
Poisson (1837) showed that the Poisson distribution is the limiting case of a binomial distribution where N approaches infinity and p goes to zero while Np = lambda.