Namespaces

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!;

Constructors

Static Functions

Methods

Properties

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

double CDF(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.

bool IsValidParameterSet(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.

double PMF(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.

double PMFLn(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.

int Sample(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.

int Sample(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.

void Samples(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.

void Samples(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

double CumulativeDistribution(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.

bool Equals(object obj)

int GetHashCode()

Type GetType()

double Probability(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.

double ProbabilityLn(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.

int Sample()

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.

void Samples(Int32[] values)

Fills an array with samples generated from the distribution.

string ToString()

Returns a String that represents this instance.
Return
string

A String that represents this instance.

Public Properties

double Entropy get;

Gets the entropy of the distribution.
Approximation, see Wikipedia

double Lambda get;

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

int Maximum get;

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

double Mean get;

Gets the mean of the distribution.

double Median get;

Gets the median of the distribution.
Approximation, see Wikipedia

int Minimum get;

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

int Mode get;

Gets the mode of the distribution.

Random RandomSource get; set;

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

double Skewness get;

Gets the skewness of the distribution.

double StdDev get;

Gets the standard deviation of the distribution.

double Variance get;

Gets the variance of the distribution.