Types in MathNet.Numerics.Distributions

Type TruncatedPareto

Namespace MathNet.Numerics.Distributions

Interfaces IContinuousDistribution

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

doubleCDF(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.

doubleInvCDF(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.

boolIsValidParameterSet(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.

doublePDF(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.

doublePDFLn(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.

doubleSample(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.

voidSamples(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

doubleCumulativeDistribution(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.

doubleDensity(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.

doubleDensityLn(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.

doubleGetMoment(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.

doubleInvCDF(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.

doubleSample()

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.

voidSamples(Double[] values)

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

The array to fill with the samples.

stringToString()

A string representation of the distribution.
Return
string

a string representation of the distribution.

Public Properties

doubleEntropy get;

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

doubleMaximum get;

Gets the maximum of the truncated Pareto distribution.

doubleMean get;

Gets the mean of the truncated Pareto distribution.

doubleMedian get;

Gets the median of the truncated Pareto distribution.

doubleMinimum get;

Gets the minimum of the truncated Pareto distribution.

doubleMode get;

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

RandomRandomSource get; set;

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

doubleScale get;

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

doubleShape get;

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

doubleSkewness get;

Gets the skewness of the truncated Pareto distribution.

doubleStdDev get;

Gets the standard deviation of the truncated Pareto distribution.

doubleTruncation get;

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

doubleVariance get;

Gets the variance of the truncated Pareto distribution.