Namespaces

Types in MathNet.Numerics.Distributions

Type Pareto

Namespace MathNet.Numerics.Distributions

Interfaces IContinuousDistribution

Continuous Univariate Pareto distribution. The Pareto distribution is a power law probability distribution that coincides with social, scientific, geophysical, actuarial, and many other types of observable phenomena. For details about this distribution, see.

Constructors

Static Functions

Methods

Properties

Public Constructors

Pareto(double scale, double shape, Random randomSource)

Initializes a new instance of the Pareto class.
Parameters
double scale

The scale (xm) of the distribution. Range: xm > 0.

double shape

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

Random randomSource

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

Pareto(double scale, double shape)

Initializes a new instance of the Pareto class.
Parameters
double scale

The scale (xm) of the distribution. Range: xm > 0.

double shape

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

Public Static Functions

double CDF(double scale, double shape, double x)

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

The scale (xm) of the distribution. Range: xm > 0.

double shape

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

double x

The location at which to compute the cumulative distribution function.

Return
double

the cumulative distribution at location x.

double InvCDF(double scale, double shape, double p)

Computes the inverse of the cumulative distribution function (InvCDF) for the distribution at the given probability. This is also known as the quantile or percent point function.
Parameters
double scale

The scale (xm) of the distribution. Range: xm > 0.

double shape

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

double p

The location at which to compute the inverse cumulative density.

Return
double

the inverse cumulative density at p.

bool IsValidParameterSet(double scale, double shape)

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

The scale (xm) of the distribution. Range: xm > 0.

double shape

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

double PDF(double scale, double shape, double x)

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

The scale (xm) of the distribution. Range: xm > 0.

double shape

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

double x

The location at which to compute the density.

Return
double

the density at x.

double PDFLn(double scale, double shape, double x)

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

The scale (xm) of the distribution. Range: xm > 0.

double shape

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

double x

The location at which to compute the density.

Return
double

the log density at x.

double Sample(double scale, double shape)

Generates a sample from the distribution.
Parameters
double scale

The scale (xm) of the distribution. Range: xm > 0.

double shape

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

Return
double

a sample from the distribution.

double Sample(Random rnd, double scale, double shape)

Generates a sample from the distribution.
Parameters
Random rnd

The random number generator to use.

double scale

The scale (xm) of the distribution. Range: xm > 0.

double shape

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

Return
double

a sample from the distribution.

IEnumerable<double> Samples(Random rnd, double scale, double shape)

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

The random number generator to use.

double scale

The scale (xm) of the distribution. Range: xm > 0.

double shape

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

Return
IEnumerable<double>

a sequence of samples from the distribution.

IEnumerable<double> Samples(double scale, double shape)

Generates a sequence of samples from the distribution.
Parameters
double scale

The scale (xm) of the distribution. Range: xm > 0.

double shape

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

Return
IEnumerable<double>

a sequence of samples from the distribution.

void Samples(Double[] values, double scale, double shape)

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

The array to fill with the samples.

double scale

The scale (xm) of the distribution. Range: xm > 0.

double shape

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

Return
void

a sequence of samples from the distribution.

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

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 scale

The scale (xm) of the distribution. Range: xm > 0.

double shape

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

Return
void

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 InverseCumulativeDistribution(double p)

Computes the inverse of the cumulative distribution function (InvCDF) for the distribution at the given probability. This is also known as the quantile or percent point function.
Parameters
double p

The location at which to compute the inverse cumulative density.

Return
double

the inverse cumulative density at p.

double Sample()

Draws a random sample from the distribution.
Return
double

A random number from this distribution.

IEnumerable<double> Samples()

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

a sequence of samples from the distribution.

void Samples(Double[] values)

Fills an array with samples generated 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 of the distribution.

double Mean get;

Gets the mean of the distribution.

double Median get;

Gets the median of the distribution.

double Minimum get;

Gets the minimum of the distribution.

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 Scale get;

Gets the scale (xm) of the distribution. Range: xm > 0.

double Shape get;

Gets the shape (α) of the distribution. Range: α > 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.