## Types in MathNet.Numerics.Distributions

Type Poisson

Namespace MathNet.Numerics.Distributions

Interfaces IDiscreteDistribution

Discrete Univariate Poisson distribution.

Distribution is described at.

Knuth's method is used to generate Poisson distributed random variables.

f(x) = exp(-λ)*λ^x/x!;

### Public Constructors

#### Poisson(double lambda, Random randomSource)

Initializes a new instance of the Poisson class.
##### Parameters
###### `double` lambda

The lambda (λ) parameter of the Poisson distribution. Range: λ > 0.

###### `Random` randomSource

The random number generator which is used to draw random samples.

#### Poisson(double lambda)

Initializes a new instance of the Poisson class.
##### Parameters
###### `double` lambda

The lambda (λ) parameter of the Poisson distribution. Range: λ > 0.

### Public Static Functions

#### doubleCDF(double lambda, double x)

Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
##### Parameters
###### `double` lambda

The lambda (λ) parameter of the Poisson distribution. Range: λ > 0.

###### `double` x

The location at which to compute the cumulative distribution function.

##### Return
###### `double`

the cumulative distribution at location x.

#### boolIsValidParameterSet(double lambda)

Tests whether the provided values are valid parameters for this distribution.
##### Parameters
###### `double` lambda

The lambda (λ) parameter of the Poisson distribution. Range: λ > 0.

#### doublePMF(double lambda, int k)

Computes the probability mass (PMF) at k, i.e. P(X = k).
##### Parameters
###### `double` lambda

The lambda (λ) parameter of the Poisson distribution. Range: λ > 0.

###### `int` k

The location in the domain where we want to evaluate the probability mass function.

##### Return
###### `double`

the probability mass at location k.

#### doublePMFLn(double lambda, int k)

Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
##### Parameters
###### `double` lambda

The lambda (λ) parameter of the Poisson distribution. Range: λ > 0.

###### `int` k

The location in the domain where we want to evaluate the log probability mass function.

##### Return
###### `double`

the log probability mass at location k.

#### intSample(Random rnd, double lambda)

Samples a Poisson distributed random variable.
##### Parameters
###### `Random` rnd

The random number generator to use.

###### `double` lambda

The lambda (λ) parameter of the Poisson distribution. Range: λ > 0.

##### Return
###### `int`

A sample from the Poisson distribution.

#### intSample(double lambda)

Samples a Poisson distributed random variable.
##### Parameters
###### `double` lambda

The lambda (λ) parameter of the Poisson distribution. Range: λ > 0.

##### Return
###### `int`

A sample from the Poisson distribution.

#### voidSamples(Int32[] values, double lambda)

Fills an array with samples generated from the distribution.
##### Parameters
###### `Int32[]` values

The array to fill with the samples.

###### `double` lambda

The lambda (λ) parameter of the Poisson distribution. Range: λ > 0.

##### Return
###### `void`

a sequence of samples from the distribution.

#### voidSamples(Random rnd, Int32[] values, double lambda)

Fills an array with samples generated from the distribution.
##### Parameters
###### `Random` rnd

The random number generator to use.

###### `Int32[]` values

The array to fill with the samples.

###### `double` lambda

The lambda (λ) parameter of the Poisson distribution. Range: λ > 0.

##### Return
###### `void`

a sequence of samples from the distribution.

#### IEnumerable<int>Samples(Random rnd, double lambda)

Samples a sequence of Poisson distributed random variables.
##### Parameters
###### `Random` rnd

The random number generator to use.

###### `double` lambda

The lambda (λ) parameter of the Poisson distribution. Range: λ > 0.

##### Return
###### `IEnumerable<int>`

a sequence of samples from the distribution.

#### IEnumerable<int>Samples(double lambda)

Samples a sequence of Poisson distributed random variables.
##### Parameters
###### `double` lambda

The lambda (λ) parameter of the Poisson distribution. Range: λ > 0.

##### Return
###### `IEnumerable<int>`

a sequence of samples from the distribution.

### Public Methods

#### doubleCumulativeDistribution(double x)

Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
##### Parameters
###### `double` x

The location at which to compute the cumulative distribution function.

##### Return
###### `double`

the cumulative distribution at location x.

#### doubleProbability(int k)

Computes the probability mass (PMF) at k, i.e. P(X = k).
##### Parameters
###### `int` k

The location in the domain where we want to evaluate the probability mass function.

##### Return
###### `double`

the probability mass at location k.

#### doubleProbabilityLn(int k)

Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
##### Parameters
###### `int` k

The location in the domain where we want to evaluate the log probability mass function.

##### Return
###### `double`

the log probability mass at location k.

#### intSample()

Samples a Poisson distributed random variable.
##### Return
###### `int`

A sample from the Poisson distribution.

#### IEnumerable<int>Samples()

Samples an array of Poisson distributed random variables.
##### Return
###### `IEnumerable<int>`

a sequence of successes in N trials.

#### voidSamples(Int32[] values)

Fills an array with samples generated from the distribution.

#### stringToString()

Returns a String that represents this instance.
##### Return
###### `string`

A String that represents this instance.

### Public Properties

#### doubleEntropy get;

Gets the entropy of the distribution.
Approximation, see Wikipedia

#### doubleLambda get;

Gets the Poisson distribution parameter λ. Range: λ > 0.

#### intMaximum get;

Gets the largest element in the domain of the distributions which can be represented by an integer.

#### doubleMean get;

Gets the mean of the distribution.

#### doubleMedian get;

Gets the median of the distribution.
Approximation, see Wikipedia

#### intMinimum get;

Gets the smallest element in the domain of the distributions which can be represented by an integer.

#### intMode get;

Gets the mode of the distribution.

#### RandomRandomSource get; set;

Gets the random number generator which is used to draw random samples.

#### doubleSkewness get;

Gets the skewness of the distribution.

#### doubleStdDev get;

Gets the standard deviation of the distribution.

#### doubleVariance get;

Gets the variance of the distribution.