## 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.

### 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

#### doubleCDF(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.

#### doubleInvCDF(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.

#### boolIsValidParameterSet(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.

#### doublePDF(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.

#### doublePDFLn(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.

#### doubleSample(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.

#### doubleSample(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.

#### voidSamples(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.

#### voidSamples(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

#### 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.

#### doubleInverseCumulativeDistribution(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.

#### doubleSample()

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.

#### voidSamples(Double[] values)

Fills an array with samples generated from the distribution.

#### stringToString()

A string representation of the distribution.
##### Return
###### `string`

a string representation of the distribution.

### Public Properties

#### doubleEntropy get;

Gets the entropy of the distribution.

#### doubleMaximum get;

Gets the maximum of the distribution.

#### doubleMean get;

Gets the mean of the distribution.

#### doubleMedian get;

Gets the median of the distribution.

#### doubleMinimum get;

Gets the minimum of the distribution.

#### doubleMode get;

Gets the mode of the distribution.

#### RandomRandomSource get; set;

Gets or sets 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 distribution.

#### doubleStdDev get;

Gets the standard deviation of the distribution.

#### doubleVariance get;

Gets the variance of the distribution.