Struct Pareto

A Pareto distribution over the real numbers from lowerBound to infinity.

Inherited Members
Namespace: Microsoft.ML.Probabilistic.Distributions
Assembly: Microsoft.ML.Probabilistic.dll
Syntax
[Serializable]
[DataContract]
[Quality(QualityBand.Preview)]
public struct Pareto : IDistribution<double>, IDistribution, ICloneable, Diffable, SettableToUniform, HasPoint<double>, CanGetLogProb<double>, SettableTo<Pareto>, SettableToProduct<Pareto>, SettableToProduct<Pareto, Pareto>, Sampleable<double>, SettableToRatio<Pareto>, SettableToRatio<Pareto, Pareto>, SettableToPower<Pareto>, SettableToWeightedSum<Pareto>, CanGetLogAverageOf<Pareto>, CanGetLogAverageOfPower<Pareto>, CanGetAverageLog<Pareto>
Remarks

The distribution has two parameters (shape, lowerBound) which must be positive for the distribution to be proper.
Its density function is p(x) = s L^s / x^(s+1) for x >= L. If shape = -1, the distribution is uniform. If shape = infinity, the distribution is a point mass on the lowerBound.

Constructors

Pareto(Pareto)

Copy constructor.

Declaration
public Pareto(Pareto that)
Parameters
Type Name Description
Pareto that

Pareto(Double, Double)

Creates a Pareto distribution with the given parameters.

Declaration
[Construction(new string[]{"Shape", "LowerBound"})]
public Pareto(double shape, double lowerBound)
Parameters
Type Name Description
Double shape
Double lowerBound

Fields

LowerBound

The lower bound

Declaration
[DataMember]
public double LowerBound
Field Value
Type Description
Double

Shape

The shape parameter

Declaration
[DataMember]
public double Shape
Field Value
Type Description
Double

Properties

IsPointMass

Declaration
[IgnoreDataMember]
public readonly bool IsPointMass { get; }
Property Value
Type Description
Boolean

Point

Declaration
[IgnoreDataMember]
public double Point { get; set; }
Property Value
Type Description
Double

Methods

Clone()

Declaration
public object Clone()
Returns
Type Description
Object

Equals(Object)

Declaration
public override bool Equals(object that)
Parameters
Type Name Description
Object that
Returns
Type Description
Boolean
Overrides

GetAverageLog(Pareto)

Declaration
public double GetAverageLog(Pareto that)
Parameters
Type Name Description
Pareto that
Returns
Type Description
Double

GetHashCode()

Declaration
public override int GetHashCode()
Returns
Type Description
Int32
Overrides

GetLogAverageOf(Pareto)

Declaration
public double GetLogAverageOf(Pareto that)
Parameters
Type Name Description
Pareto that
Returns
Type Description
Double

GetLogAverageOfPower(Pareto, Double)

Declaration
public double GetLogAverageOfPower(Pareto that, double power)
Parameters
Type Name Description
Pareto that
Double power
Returns
Type Description
Double

GetLogNormalizer()

Declaration
public double GetLogNormalizer()
Returns
Type Description
Double

GetLogProb(Double)

Declaration
public double GetLogProb(double value)
Parameters
Type Name Description
Double value
Returns
Type Description
Double

IsProper()

Declaration
public bool IsProper()
Returns
Type Description
Boolean

IsUniform()

Declaration
public bool IsUniform()
Returns
Type Description
Boolean

MaxDiff(Object)

Declaration
public double MaxDiff(object that)
Parameters
Type Name Description
Object that
Returns
Type Description
Double

Sample()

Declaration
public double Sample()
Returns
Type Description
Double

Sample(Double)

Declaration
public double Sample(double result)
Parameters
Type Name Description
Double result
Returns
Type Description
Double

SetTo(Pareto)

Declaration
public void SetTo(Pareto that)
Parameters
Type Name Description
Pareto that

SetToPower(Pareto, Double)

Declaration
public void SetToPower(Pareto value, double exponent)
Parameters
Type Name Description
Pareto value
Double exponent

SetToProduct(Pareto, Pareto)

Declaration
public void SetToProduct(Pareto a, Pareto b)
Parameters
Type Name Description
Pareto a
Pareto b

SetToRatio(Pareto, Pareto, Boolean)

Declaration
public void SetToRatio(Pareto numerator, Pareto denominator, bool forceProper = false)
Parameters
Type Name Description
Pareto numerator
Pareto denominator
Boolean forceProper

SetToSum(Double, Pareto, Double, Pareto)

Declaration
public void SetToSum(double weight1, Pareto value1, double weight2, Pareto value2)
Parameters
Type Name Description
Double weight1
Pareto value1
Double weight2
Pareto value2

SetToUniform()

Declaration
public void SetToUniform()

ToString()

Declaration
public override string ToString()
Returns
Type Description
String
Overrides

Uniform()

Creates a uniform Pareto distribution.

Declaration
public static Pareto Uniform()
Returns
Type Description
Pareto

Operators

Multiply(Pareto, Pareto)

Static product operator. Create a Pareto distribution which is the product of two Pareto distributions

Declaration
public static Pareto operator *(Pareto a, Pareto b)
Parameters
Type Name Description
Pareto a

The first distribution
Pareto b

The second distribution
Returns
Type Description
Pareto

The resulting distribution

Implements