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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
SystemObject
  CenterSpace.NMath.CoreProbabilityDistribution
    CenterSpace.NMath.CorePoissonDistribution

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

The PoissonDistribution type exposes the following members.

Constructors
 NameDescription
Public methodPoissonDistribution Constructs a PoissonDistribution with the specified lambda, which is both the mean and the variance of the distribution.
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Properties
 NameDescription
Public propertyKurtosis Gets the kurtosis, a measure of the degree of peakednesss of the distribution.
Public propertyMean Gets and sets the mean of the distribution.
Public propertySkewness Gets the skewness, a measure of the degree of asymmetry of this distribution.
Public propertyVariance Gets and sets the variance of the distribution.
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Methods
 NameDescription
Public methodCDF Returns the cumulative distribution function evaluated at a given value.
(Overrides ProbabilityDistributionCDF(Double))
Public methodClone Creates a deep copy of this PoissonDistribution.
(Overrides ProbabilityDistributionClone)
Public methodInverseCDF Returns the inverse cumulative distribution function evaluated at a given value.
(Overrides ProbabilityDistributionInverseCDF(Double))
Protected methodInverseCdfUsingBracket Uses a bracketing method to evaluate the inverse of cumulative distribution functions.
(Inherited from ProbabilityDistribution)
Protected methodInverseDiscreteCdfUsingBracket Uses a bracketing method to evaluate the inverse of cumulative distribution functions for discrete distributions.
(Inherited from ProbabilityDistribution)
Public methodPDF Returns the probability density function evaluated at a given value.
(Overrides ProbabilityDistributionPDF(Double))
Public methodToString 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:
C#
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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.
See Also