Namespaces

Types in MathNet.Numerics.Distributions

Type TruncatedPareto

Namespace MathNet.Numerics.Distributions

Interfaces IContinuousDistribution

Constructors

Static Functions

Methods

Properties

Public Constructors

TruncatedPareto(double scale, double shape, double truncation, Random randomSource)

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

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

double shape

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

double truncation

The truncation (T) of the distribution. Range: T > xm.

Random randomSource

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

Public Static Functions

double CDF(double scale, double shape, double truncation, 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 truncation

The truncation (T) of the distribution. Range: T > xm.

double x

The location at which to compute the cumulative distribution function.

Return
double

the cumulative distribution at location x.

double ICDF(double scale, double shape, double truncation, double p)

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

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

double shape

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

double truncation

The truncation (T) of the distribution. Range: T > xm.

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 scale, double shape, double truncation)

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 truncation

The truncation (T) of the distribution. Range: T > xm.

double PDF(double scale, double shape, double truncation, 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 truncation

The truncation (T) of the distribution. Range: T > xm.

double x

The location at which to compute the density.

Return
double

the density at x.

double PDFLn(double scale, double shape, double truncation, 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 truncation

The truncation (T) of the distribution. Range: T > xm.

double x

The location at which to compute the log density.

Return
double

the log density at x.

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

Generates a sample from the truncated Pareto 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.

double truncation

The truncation (T) of the distribution. Range: T > xm.

Return
double

a sample from the distribution.

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

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.

double truncation

The truncation (T) of the distribution. Range: T > xm.

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

Generates a sequence of samples from the truncated Pareto 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.

double truncation

The truncation (T) of the distribution. Range: T > xm.

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()

double GetMoment(int n)

Gets the n-th raw moment of the distribution.
Parameters
int n

The order (n) of the moment. Range: n ≥ 1.

Return
double

the n-th moment of the distribution.

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 truncated Pareto distribution.
Return
double

a sample from the distribution.

IEnumerable<double> Samples()

Generates a sequence of samples from the truncated 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.
Parameters
Double[] values

The array to fill with the samples.

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 truncated Pareto distribution (not supported).

double Maximum get;

Gets the maximum of the truncated Pareto distribution.

double Mean get;

Gets the mean of the truncated Pareto distribution.

double Median get;

Gets the median of the truncated Pareto distribution.

double Minimum get;

Gets the minimum of the truncated Pareto distribution.

double Mode get;

Gets the mode of the truncated Pareto distribution (not supported).

Random RandomSource get; set;

Gets 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 truncated Pareto distribution.

double StdDev get;

Gets the standard deviation of the truncated Pareto distribution.

double Truncation get;

Gets the truncation (T) of the distribution. Range: T > 0.

double Variance get;

Gets the variance of the truncated Pareto distribution.