ParetoDistribution Class

Represents the Pareto distribution.

Definition

Namespace: Numerics.NET.Statistics.Distributions
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.2

[SerializableAttribute]
public class ParetoDistribution : ContinuousDistribution

Visual Basic

<SerializableAttribute>
Public Class ParetoDistribution
	Inherits ContinuousDistribution

C++/CLI

[SerializableAttribute]
public ref class ParetoDistribution : public ContinuousDistribution

[<SerializableAttribute>]
type ParetoDistribution = 
    class
        inherit ContinuousDistribution
    end

Inheritance: Object → Distribution → ContinuousDistribution → ParetoDistribution

Remarks

The Pareto distribution is a skewed, heavy-tailed distribution that is sometimes used to model the distribution of incomes.

Constructors

ParetoDistribution(Double, Double)	Constructs a new one-parameter ParetoDistribution using the specified shape parameters.
ParetoDistribution(Double, Double, ParetoDistributionVariant)	Constructs a new ParetoDistribution using the specified shape parameters.

Properties

Capabilities	Gets a value that indicates the capabilities of the distribution class. (Inherited from Distribution)
Entropy	Gets the entropy of the distribution. (Overrides Distribution.Entropy)
InterQuartileRange	Returns the inter-quartile range of this distribution. (Inherited from ContinuousDistribution)
IsSymmetrical	Gets whether the distribution is known to be symmetrical around the mean. (Inherited from ContinuousDistribution)
IsUnimodal	Gets whether the distribution has one or more modes. (Inherited from ContinuousDistribution)
Kurtosis	Gets the kurtosis of the distribution. (Overrides Distribution.Kurtosis)
Mean	Gets the mean or expectation value of the distribution. (Overrides Distribution.Mean)
Median	Gets the median of the distribution. (Overrides ContinuousDistribution.Median)
Mode	Gets the mode of the distribution. (Overrides ContinuousDistribution.Mode)
NumberOfModes	Gets the number of modes of the distribution. (Inherited from ContinuousDistribution)
ScaleParameter	Gets the scale parameter for the distribution.
ShapeParameter	Gets the shape parameter for the distribution.
Skewness	Gets the skewness of the distribution. (Overrides Distribution.Skewness)
StandardDeviation	Gets the standard deviation of the distribution. (Inherited from Distribution)
StatisticSymbol	Gets the common symbol to describe a statistic from the distribution. (Inherited from Distribution)
Support	Gets the support of the distribution. (Overrides ContinuousDistribution.Support)
Variance	Gets the variance of the distribution. (Overrides Distribution.Variance)
Variant	Gets whether the distribution is a one or two parameter Pareto distribution.

Methods

Cdf	Evaluates the cumulative distribution function (CDF) of this distribution for the specified value. (Inherited from ContinuousDistribution)
DistributionFunction	Evaluates the cumulative distribution function (CDF) of this distribution for the specified value. (Overrides ContinuousDistribution.DistributionFunction(Double))
Equals	Determines whether the specified object is equal to the current object. (Inherited from Object)
Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object)
GetAllModes	Returns an array that contains all the modes of the distribution. (Inherited from ContinuousDistribution)
GetExpectationValue(Func<Double, Double>)	Returns the expectation value of a function. (Inherited from ContinuousDistribution)
GetExpectationValue(Func<Double, Double>, Double, Double)	Returns the un-normalized expectation value of a function over the specified interval. (Inherited from ContinuousDistribution)
GetExpectedHistogram(Double[], Double)	Gets a vector containing a histogram of the expected number of samples for a given total number of samples. (Inherited from ContinuousDistribution)
GetExpectedHistogram(IntervalIndex<Double>, Double)	Gets a vector containing a histogram of the expected number of samples for a given total number of samples. (Inherited from ContinuousDistribution)
GetExpectedHistogram(Double, Double, Int32, Double)	Gets a vector whose bins contain the expected number of samples for a given total number of samples. (Inherited from ContinuousDistribution)
GetHashCode	Serves as the default hash function. (Inherited from Object)
GetRandomSequence()	Returns a sequence of random samples from the distribution. (Inherited from ContinuousDistribution)
GetRandomSequence(Random)	Returns a sequence of random samples from the distribution. (Inherited from ContinuousDistribution)
GetRandomSequence(Random, Int32)	Returns a sequence of random samples of the specified length from the distribution. (Inherited from ContinuousDistribution)
GetType	Gets the Type of the current instance. (Inherited from Object)
HazardFunction	Returns the probability of failure at the specified value. (Inherited from ContinuousDistribution)
InverseCdf	Returns the inverse of the DistributionFunction(Double). (Inherited from ContinuousDistribution)
InverseDistributionFunction	Returns the inverse of the DistributionFunction(Double). (Overrides ContinuousDistribution.InverseDistributionFunction(Double))
LeftTailProbability	Returns the probability that a sample from the distribution is less than the specified value. (Inherited from ContinuousDistribution)
LogProbabilityDensityFunction	Returns the logarithm of the probability density function (PDF) of this distribution for the specified value. (Overrides ContinuousDistribution.LogProbabilityDensityFunction(Double))
MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object)
MomentFunction	Returns the value of the moment function of the specified order. (Overrides ContinuousDistribution.MomentFunction(Int32, Double))
Pdf	Returns the value of the probability density function (PDF) of this distribution for the specified value. (Inherited from ContinuousDistribution)
Probability	Returns the probability that a sample taken from the distribution lies inside the specified interval. (Inherited from ContinuousDistribution)
ProbabilityDensityFunction	Returns the value of the probability density function (PDF) of this distribution for the specified value. (Overrides ContinuousDistribution.ProbabilityDensityFunction(Double))
RightTailProbability	Returns the probability that a sample from the distribution is larger than the specified value. (Inherited from ContinuousDistribution)
Sample()	Returns a random sample from the distribution. (Inherited from ContinuousDistribution)
Sample(Int32)	Returns a vector of random samples from the distribution. (Inherited from ContinuousDistribution)
Sample(Random)	Returns a random sample from the distribution. (Overrides ContinuousDistribution.Sample(Random))
Sample(Int32, Random)	Returns a vector of random samples from the distribution. (Inherited from ContinuousDistribution)
Sample(Random, Double, Double)	Returns a single random sample from a Pareto distribution with the specified parameters.
SampleInto(Random, IList<Double>)	Fills a list with random numbers from the distribution. (Inherited from ContinuousDistribution)
SampleInto(Random, Double[])	Fills a list with random numbers from the distribution. (Inherited from ContinuousDistribution)
SampleInto(Random, Span<Double>)	Fills a span with random numbers from the distribution. (Inherited from ContinuousDistribution)
SampleInto(Random, IList<Double>, Int32, Int32)	Fills part of a list with random numbers from the distribution. (Inherited from ContinuousDistribution)
SurvivorDistributionFunction	Evaluates the survivor distribution function (SDF) of this distribution for the specified value. (Inherited from ContinuousDistribution)
ToString	Returns a string that represents the current object. (Inherited from Object)
TwoTailedProbability	Returns the probability that a sample from the distribution deviates from the mean more than the specified value. (Inherited from ContinuousDistribution)