Namespaces

Types in MathNet.Numerics.Distributions

Type InverseGaussian

Namespace MathNet.Numerics.Distributions

Interfaces IContinuousDistribution

Constructors

Static Functions

Methods

Properties

Public Constructors

InverseGaussian(double mu, double lambda, Random randomSource)

Initializes a new instance of the InverseGaussian class.
Parameters
double mu

The mean (μ) of the distribution. Range: μ > 0.

double lambda

The shape (λ) of the distribution. Range: λ > 0.

Random randomSource

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

Public Static Functions

double CDF(double mu, double lambda, double x)

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

The mean (μ) of the distribution. Range: μ > 0.

double lambda

The shape (λ) of the distribution. Range: λ > 0.

double x

The location at which to compute the cumulative distribution function.

Return
double

the cumulative distribution at location x.

InverseGaussian Estimate(IEnumerable<double> samples, Random randomSource)

Estimates the Inverse Gaussian parameters from sample data with maximum-likelihood.
Parameters
IEnumerable<double> samples

The samples to estimate the distribution parameters from.

Random randomSource

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

Return
InverseGaussian

An Inverse Gaussian distribution.

double ICDF(double mu, double lambda, double p)

Computes the inverse cumulative distribution (CDF) of the distribution at p, i.e. solving for P(X ≤ x) = p.
Parameters
double mu

The mean (μ) of the distribution. Range: μ > 0.

double lambda

The shape (λ) of the distribution. Range: λ > 0.

double p

The location at which to compute the inverse cumulative distribution function.

Return
double

the inverse cumulative distribution at location p.

bool IsValidParameterSet(double mu, double lambda)

Tests whether the provided values are valid parameters for this distribution.
Parameters
double mu

The mean (μ) of the distribution. Range: μ > 0.

double lambda

The shape (λ) of the distribution. Range: λ > 0.

double PDF(double mu, double lambda, double x)

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

The mean (μ) of the distribution. Range: μ > 0.

double lambda

The shape (λ) of the distribution. Range: λ > 0.

double x

The location at which to compute the density.

Return
double

the density at x.

double PDFLn(double mu, double lambda, double x)

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

The mean (μ) of the distribution. Range: μ > 0.

double lambda

The shape (λ) of the distribution. Range: λ > 0.

double x

The location at which to compute the log density.

Return
double

the log density at x.

double Sample(Random rnd, double mu, double lambda)

Generates a sample from the inverse Gaussian distribution.
Parameters
Random rnd

The random number generator to use.

double mu

The mean (μ) of the distribution. Range: μ > 0.

double lambda

The shape (λ) of the distribution. Range: λ > 0.

Return
double

a sample from the distribution.

void Samples(Random rnd, Double[] values, double mu, double lambda)

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.

double mu

The mean (μ) of the distribution. Range: μ > 0.

double lambda

The shape (λ) of the distribution. Range: λ > 0.

IEnumerable<double> Samples(Random rnd, double mu, double lambda)

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

The random number generator to use.

double mu

The mean (μ) of the distribution. Range: μ > 0.

double lambda

The shape (λ) of the distribution. Range: λ > 0.

Return
IEnumerable<double>

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.

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 InvCDF(double p)

Computes the inverse cumulative distribution (CDF) of the distribution at p, i.e. solving for P(X ≤ x) = p.
Parameters
double p

The location at which to compute the inverse cumulative distribution function.

Return
double

the inverse cumulative distribution at location p.

double Sample()

Generates a sample from the inverse Gaussian distribution.
Return
double

a sample from the distribution.

void Samples(Double[] values)

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

The array to fill with the samples.

IEnumerable<double> Samples()

Generates a sequence of samples from the inverse Gaussian 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 Inverse Gaussian distribution (currently not supported).

double Kurtosis get;

Gets the kurtosis of the Inverse Gaussian distribution.

double Lambda get;

Gets the shape (λ) of the distribution. Range: λ > 0.

double Maximum get;

Gets the maximum of the Inverse Gaussian distribution.

double Mean get;

Gets the mean of the Inverse Gaussian distribution.

double Median get;

Gets the median of the Inverse Gaussian distribution. No closed form analytical expression exists, so this value is approximated numerically and can throw an exception.

double Minimum get;

Gets the minimum of the Inverse Gaussian distribution.

double Mode get;

Gets the mode of the Inverse Gaussian distribution.

double Mu get;

Gets the mean (μ) of the distribution. Range: μ > 0.

Random RandomSource get; set;

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

double Skewness get;

Gets the skewness of the Inverse Gaussian distribution.

double StdDev get;

Gets the standard deviation of the Inverse Gaussian distribution.

double Variance get;

Gets the variance of the Inverse Gaussian distribution.