Namespaces

Types in MathNet.Numerics.Distributions

Type Erlang

Namespace MathNet.Numerics.Distributions

Interfaces IContinuousDistribution

Continuous Univariate Erlang distribution. This distribution is a continuous probability distribution with wide applicability primarily due to its relation to the exponential and Gamma distributions..

Constructors

Static Functions

Methods

Properties

Public Constructors

Erlang(int shape, double rate, Random randomSource)

Initializes a new instance of the Erlang class.
Parameters
int shape

The shape (k) of the Erlang distribution. Range: k ≥ 0.

double rate

The rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.

Random randomSource

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

Erlang(int shape, double rate)

Initializes a new instance of the Erlang class.
Parameters
int shape

The shape (k) of the Erlang distribution. Range: k ≥ 0.

double rate

The rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.

Public Static Functions

double CDF(int shape, double rate, double x)

Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
Parameters
int shape

The shape (k) of the Erlang distribution. Range: k ≥ 0.

double rate

The rate or inverse scale (λ) of the Erlang 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(int shape, double rate)

Tests whether the provided values are valid parameters for this distribution.
Parameters
int shape

The shape (k) of the Erlang distribution. Range: k ≥ 0.

double rate

The rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.

double PDF(int shape, double rate, double x)

Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
Parameters
int shape

The shape (k) of the Erlang distribution. Range: k ≥ 0.

double rate

The rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.

double x

The location at which to compute the density.

Return
double

the density at x.

double PDFLn(int shape, double rate, double x)

Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
Parameters
int shape

The shape (k) of the Erlang distribution. Range: k ≥ 0.

double rate

The rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.

double x

The location at which to compute the density.

Return
double

the log density at x.

double Sample(Random rnd, int shape, double rate)

Generates a sample from the distribution.
Parameters
Random rnd

The random number generator to use.

int shape

The shape (k) of the Erlang distribution. Range: k ≥ 0.

double rate

The rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.

Return
double

a sample from the distribution.

double Sample(int shape, double rate)

Generates a sample from the distribution.
Parameters
int shape

The shape (k) of the Erlang distribution. Range: k ≥ 0.

double rate

The rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.

Return
double

a sample from the distribution.

IEnumerable<double> Samples(Random rnd, int shape, double rate)

Generates a sequence of samples from the distribution.
Parameters
Random rnd

The random number generator to use.

int shape

The shape (k) of the Erlang distribution. Range: k ≥ 0.

double rate

The rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.

Return
IEnumerable<double>

a sequence of samples from the distribution.

void Samples(Random rnd, Double[] values, int shape, double rate)

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

The random number generator to use.

Double[] values

The array to fill with the samples.

int shape

The shape (k) of the Erlang distribution. Range: k ≥ 0.

double rate

The rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.

Return
void

a sequence of samples from the distribution.

IEnumerable<double> Samples(int shape, double rate)

Generates a sequence of samples from the distribution.
Parameters
int shape

The shape (k) of the Erlang distribution. Range: k ≥ 0.

double rate

The rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.

Return
IEnumerable<double>

a sequence of samples from the distribution.

void Samples(Double[] values, int shape, double rate)

Fills an array with samples generated from the distribution.
Parameters
Double[] values

The array to fill with the samples.

int shape

The shape (k) of the Erlang distribution. Range: k ≥ 0.

double rate

The rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.

Return
void

a sequence of samples from the distribution.

Erlang WithShapeRate(int shape, double rate, Random randomSource)

Constructs a Erlang distribution from a shape and inverse scale parameter. The distribution will be initialized with the default random number generator.
Parameters
int shape

The shape (k) of the Erlang distribution. Range: k ≥ 0.

double rate

The rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.

Random randomSource

The random number generator which is used to draw random samples. Optional, can be null.

Erlang WithShapeScale(int shape, double scale, Random randomSource)

Constructs a Erlang distribution from a shape and scale parameter. The distribution will be initialized with the default random number generator.
Parameters
int shape

The shape (k) of the Erlang distribution. Range: k ≥ 0.

double scale

The scale (μ) of the Erlang distribution. Range: μ ≥ 0.

Random randomSource

The random number generator which is used to draw random samples. Optional, can be null.

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.

double Density(double x)

Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x.
Parameters
double x

The location at which to compute the density.

Return
double

the density at x.

double DensityLn(double x)

Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x).
Parameters
double x

The location at which to compute the log density.

Return
double

the log density at x.

bool Equals(object obj)

int GetHashCode()

Type GetType()

double Sample()

Generates a sample from the Erlang distribution.
Return
double

a sample from the distribution.

void Samples(Double[] values)

Fills an array with samples generated from the distribution.

IEnumerable<double> Samples()

Generates a sequence of samples from the Erlang distribution.
Return
IEnumerable<double>

a sequence of samples from the distribution.

string ToString()

A string representation of the distribution.
Return
string

a string representation of the distribution.

Public Properties

double Entropy get;

Gets the entropy of the distribution.

double Maximum get;

Gets the Maximum value.

double Mean get;

Gets the mean of the distribution.

double Median get;

Gets the median of the distribution.

double Minimum get;

Gets the minimum value.

double Mode get;

Gets the mode of the distribution.

Random RandomSource get; set;

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

double Rate get;

Gets the rate or inverse scale (λ) of the Erlang distribution. Range: λ ≥ 0.

double Scale get;

Gets the scale of the Erlang distribution.

int Shape get;

Gets the shape (k) of the Erlang distribution. Range: k ≥ 0.

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.