[DataContract]
[Quality(QualityBand.Experimental)]
public class LeftTruncatedPoisson : IDistribution<int>, IDistribution, ICloneable, Diffable, SettableToUniform, HasPoint<int>, CanGetLogProb<int>, CanGetMean<double>, Sampleable<int>, SettableToProduct<LeftTruncatedPoisson>, SettableToProduct<LeftTruncatedPoisson, LeftTruncatedPoisson>, SettableToRatio<LeftTruncatedPoisson>, SettableToRatio<LeftTruncatedPoisson, LeftTruncatedPoisson>, SettableToPower<LeftTruncatedPoisson>, SettableToWeightedSum<LeftTruncatedPoisson>, SettableTo<LeftTruncatedPoisson>, SettableTo<Discrete>, SettableToPartialUniform<LeftTruncatedPoisson>, SettableToPartialUniform<Discrete>, CanGetLogAverageOf<LeftTruncatedPoisson>, CanGetAverageLog<LeftTruncatedPoisson>, CanGetLogNormalizer, ICanTruncateLeft<int>

Constructors

LeftTruncatedPoisson()

Initializes a new instance of the LeftTruncatedPoisson class.

Declaration

public LeftTruncatedPoisson()

LeftTruncatedPoisson(Poisson, Int32)

Initializes a new instance of the LeftTruncatedPoisson class.

Declaration

public LeftTruncatedPoisson(Poisson nonTruncatedDistribution, int startPoint)

Parameters

Type	Name	Description
Poisson	nonTruncatedDistribution	The non-truncated CoM-Poisson distribution.
Int32	startPoint	The index of the first non-zero term in the truncated distribution.

LeftTruncatedPoisson(Double, Double, Int32)

Initializes a new instance of the LeftTruncatedPoisson class.

Declaration

[Construction(new string[]{"Rate", "Precision", "StartPoint"})]
public LeftTruncatedPoisson(double rate, double precision, int startPoint)

Parameters

Type	Name	Description
Double	rate	The rate parameter of the underlying CoM-Poisson distribution.
Double	precision	The precision parameter of the underlying CoM-Poisson distribution.
Int32	startPoint	The index of the first non-zero term in the truncated distribution.

LeftTruncatedPoisson(Double, Int32)

Initializes a new instance of the LeftTruncatedPoisson class.

Declaration

public LeftTruncatedPoisson(double rate, int startPoint)

Parameters

Type	Name	Description
Double	rate	The rate parameter of the underlying Poisson distribution. The precision parameter is assumed to be 1.0.
Int32	startPoint	The index of the first non-zero term in the truncated distribution.

Fields

Tolerance

Tolerance for numerical calculations.

Declaration

public const double Tolerance = 1E-10

Field Value

Type	Description
Double

Properties

IsPointMass

Gets a value indicating whether the current distribution represents a point mass.

Declaration

public bool IsPointMass { get; }

Property Value

Type	Description
Boolean

LogNormalizer

Returns the log normalizer of the instance.

Declaration

public double LogNormalizer { get; }

Property Value

Type	Description
Double

MeanLogFactorial

Returns the mean log factorial of the instance.

Declaration

public double MeanLogFactorial { get; }

Property Value

Type	Description
Double

Point

Gets or sets the distribution as a point mass.

Declaration

public int Point { get; set; }

Property Value

Type	Description
Int32

Precision

Gets or sets the precision parameter of the COM-Poisson distribution

Declaration

public double Precision { get; set; }

Property Value

Type	Description
Double

Rate

Gets or sets the rate parameter of the COM-Poisson distribution, always >= 0.

Declaration

public double Rate { get; set; }

Property Value

Type	Description
Double

StartPoint

The first non-zero point.

Declaration

[DataMember]
public int StartPoint { get; }

Property Value

Type	Description
Int32

SumLogFactorial

Returns the log normalizer of the instance.

Declaration

public double SumLogFactorial { get; }

Property Value

Type	Description
Double

Methods

Clone()

Creates a cloned copy of this distribution.

Declaration

public object Clone()

Returns

Type	Description
Object	The copy.

FromMeanAndStartPoint(Double, Double, Int32, Double, Int32)

Initializes a new instance of the LeftTruncatedPoisson struct given a target mean and a start point.

Declaration

public static LeftTruncatedPoisson FromMeanAndStartPoint(double targetMean, double precision, int startPoint, double tolerance = 1E-10, int maxIterations = 100)

Parameters

Type	Name	Description
Double	targetMean	The desired mean of the Truncated Poisson.
Double	precision	The desired precision of the Truncated Poisson.
Int32	startPoint	The start point.
Double	tolerance	Tolerance for mean.
Int32	maxIterations	Maximum iterations for binary search.

Returns

Type	Description
LeftTruncatedPoisson	A new instance with the target mean.

GetAverageLog(LeftTruncatedPoisson)

Gets the expected logarithm of a truncated COM-Poisson under this truncated COM-Poisson.

Declaration

public double GetAverageLog(LeftTruncatedPoisson that)

Parameters

Type	Name	Description
LeftTruncatedPoisson	that	The distribution to take the logarithm of.

Returns

Type	Description
Double	`sum_x this.Evaluate(x)*Math.Log(that.Evaluate(x))`

Remarks

This is also known as the cross entropy.

GetLogAverageOf(LeftTruncatedPoisson)

Gets the log of the integral of the product of this truncated COM-Poisson with another truncated COM-Poisson.

Declaration

public double GetLogAverageOf(LeftTruncatedPoisson that)

Parameters

Type	Name	Description
LeftTruncatedPoisson	that	The other truncated COM-Poisson

Returns

Type	Description
Double

GetLogNormalizer()

Gets the log of the normalizer of this distribution.

Declaration

public double GetLogNormalizer()

Returns

Type	Description
Double	The log of the normalizer.

GetLogNormalizer(Double, Double, Int32)

Gets the log normalizer of a left-truncated Poisson. TODO: integrate this with Poisson.GetLogNormalizer.

Declaration

public static double GetLogNormalizer(double rate, double prec, int startPoint)

Parameters

Type	Name	Description
Double	rate	Rate parameter.
Double	prec	Precision parameter.
Int32	startPoint	Start point.

Returns

Type	Description
Double	The log normalizer of the distribution.

GetLogProb(Int32)

Gets the log probability for a given domain value.

Declaration

public double GetLogProb(int value)

Parameters

Type	Name	Description
Int32	value	The domain value.

Returns

Type	Description
Double	The log probability of the value.

GetLogProb(Int32, Double, Double, Double)

Gets the log probability when some calculations have been done externally.

Declaration

public static double GetLogProb(int value, double logRate, double precision, double logNormalizer)

Parameters

Type	Name	Description
Int32	value	The domain value.
Double	logRate	The log of the rate.
Double	precision	The precision.
Double	logNormalizer	The log normalizer.

Returns

Type	Description
Double	The log probability of the value.

GetMean()

Gets the mean of this distribution.

Declaration

public double GetMean()

Returns

Type	Description
Double	The mean.

GetStartPoint()

Gets the start point of the truncated distribution.

Declaration

public int GetStartPoint()

Returns

Type	Description
Int32	The start point.

GetSumLogFactorial(Double, Double, Int32)

Computes sum_{x=start..infinity} log(x!) lambda^x / x!^nu

Declaration

public static double GetSumLogFactorial(double lambda, double nu, int startPoint)

Parameters

Type	Name	Description
Double	lambda	The rate.
Double	nu	The precision.
Int32	startPoint	The start point.

Returns

Type	Description
Double	The sum log factorial.

IsPartialUniform()

Checks whether the distribution is uniform over its support.

Declaration

public bool IsPartialUniform()

Returns

Type	Description
Boolean	True if the distribution is uniform over its support, false otherwise.

IsProper()

Asks whether this instance is proper or not. A truncated COM-Poisson distribution is proper if Rate >= 0 and (Precision > 0 or (Precision == 0 and Rate < 1)).

Declaration

public bool IsProper()

Returns

Type	Description
Boolean	True if proper, false otherwise

IsUniform()

Gets a value indicating whether the current distribution is uniform.

Declaration

public bool IsUniform()

Returns

Type	Description
Boolean

MaxDiff(Object)

Gets a value indicating how close this distribution is to another distribution. in terms of probabilities they assign to sequences.

Declaration

public double MaxDiff(object that)

Parameters

Type	Name	Description
Object	that	The other distribution.

Returns

Type	Description
Double	The max difference.

PointMass(Int32)

Creates a truncated Com-Poisson distribution which only allows one value.

Declaration

[Construction(new string[]{"Point"}, UseWhen = "IsPointMass")]
public static LeftTruncatedPoisson PointMass(int value)

Parameters

Type	Name	Description
Int32	value	The value of the point mass.

Returns

Type	Description
LeftTruncatedPoisson	A point mass at the given value.

Sample()

Emits a random sample from this distribution.

Declaration

public int Sample()

Returns

Type	Description
Int32	A random sample.

Sample(Int32)

Emits a random sample from this distribution.

Declaration

public int Sample(int result)

Parameters

Type	Name	Description
Int32	result	This argument is ignored.

Returns

Type	Description
Int32	A random sample.

SetTo(Discrete)

Set the instance to have the same value as given

Declaration

public void SetTo(Discrete value)

Parameters

Type	Name	Description
Discrete	value

SetTo(LeftTruncatedPoisson)

Set the instance to have the same value as given

Declaration

public void SetTo(LeftTruncatedPoisson value)

Parameters

Type	Name	Description
LeftTruncatedPoisson	value

SetToPartialUniform()

Set non-zero support to uniform

Declaration

public void SetToPartialUniform()

SetToPartialUniform(Int32)

Sets the current distribution to be uniform beyond a given start point.

Declaration

public void SetToPartialUniform(int startPoint)

Parameters

Type	Name	Description
Int32	startPoint	The start point.

SetToPartialUniformOf(Discrete)

Sets the distribution to be uniform over the support of a given distribution.

Declaration

public void SetToPartialUniformOf(Discrete dist)

Parameters

Type	Name	Description
Discrete	dist

SetToPartialUniformOf(LeftTruncatedPoisson)

Sets the distribution to be uniform over the support of a given distribution.

Declaration

public void SetToPartialUniformOf(LeftTruncatedPoisson dist)

Parameters

Type	Name	Description
LeftTruncatedPoisson	dist

SetToPower(LeftTruncatedPoisson, Double)

Sets the parameters to represent the power of a truncated COM-Poisson to some exponent.

Declaration

public void SetToPower(LeftTruncatedPoisson dist, double exponent)

Parameters

Type	Name	Description
LeftTruncatedPoisson	dist	The source truncated COM-Poisson
Double	exponent	The exponent

SetToProduct(LeftTruncatedPoisson, LeftTruncatedPoisson)

Sets the parameters to represent the product of two truncated COM-Poissons.

Declaration

public void SetToProduct(LeftTruncatedPoisson a, LeftTruncatedPoisson b)

Parameters

Type	Name	Description
LeftTruncatedPoisson	a	The first truncated COM-Poisson
LeftTruncatedPoisson	b	The second truncated COM-Poisson

SetToRatio(LeftTruncatedPoisson, LeftTruncatedPoisson, Boolean)

Sets the parameters to represent the ratio of two truncated COM-Poisson distributions

Declaration

public void SetToRatio(LeftTruncatedPoisson numerator, LeftTruncatedPoisson denominator, bool forceProper = false)

Parameters

Type	Name	Description
LeftTruncatedPoisson	numerator	The numerator truncated distribution
LeftTruncatedPoisson	denominator	The denominator truncated distribution
Boolean	forceProper	If true, the result has precision >= 0 and rate <= 1

Remarks

The result may not be proper. No error is thrown in this case.

SetToSum(Double, LeftTruncatedPoisson, Double, LeftTruncatedPoisson)

Set the parameters to match the moments of a mixture distribution.

Declaration

public void SetToSum(double weight1, LeftTruncatedPoisson dist1, double weight2, LeftTruncatedPoisson dist2)

Parameters

Type	Name	Description
Double	weight1	The first weight
LeftTruncatedPoisson	dist1	The first distribution
Double	weight2	The second weight
LeftTruncatedPoisson	dist2	The second distribution

SetToUniform()

Sets the current distribution to be uniform.

Declaration

public void SetToUniform()

ToString()

Overrides ToString method.

Declaration

public override string ToString()

Returns

Type	Description
String	String representation of instance.

Overrides

Object.ToString()

TruncatedUniform(Int32)

Instantiates a uniform truncated Com-Poisson distribution beyond a given start point.

Declaration

public static LeftTruncatedPoisson TruncatedUniform(int startPoint)

Parameters

Type	Name	Description
Int32	startPoint	Start point.

Returns

Type	Description
LeftTruncatedPoisson	A new uniform Com-Poisson distribution

TruncateLeft(Int32)

Truncates the distribution at the given point.

Declaration

public void TruncateLeft(int startPoint)

Parameters

Type	Name	Description
Int32	startPoint

Uniform()

Instantiates a uniform truncated Com-Poisson distribution

Declaration

[Construction(UseWhen = "IsUniform")]
public static LeftTruncatedPoisson Uniform()

Returns

Type	Description
LeftTruncatedPoisson	A new uniform Com-Poisson distribution

Operators

Division(LeftTruncatedPoisson, LeftTruncatedPoisson)

Creates a new truncated COM-Poisson which is the ratio of two other truncated COM-Poissons

Declaration

public static LeftTruncatedPoisson operator /(LeftTruncatedPoisson numerator, LeftTruncatedPoisson denominator)

Parameters

Type	Name	Description
LeftTruncatedPoisson	numerator	The numerator distribution
LeftTruncatedPoisson	denominator	The denominator distribution

Returns

Type	Description
LeftTruncatedPoisson	Result of the ratio calculation.

ExclusiveOr(LeftTruncatedPoisson, Double)

Raises a truncated COM-Poisson to a power.

Declaration

public static LeftTruncatedPoisson operator ^(LeftTruncatedPoisson dist, double exponent)

Parameters

Type	Name	Description
LeftTruncatedPoisson	dist	The distribution.
Double	exponent	The power to raise to.

Returns

Type	Description
LeftTruncatedPoisson	`dist` raised to power `exponent`.

Multiply(LeftTruncatedPoisson, LeftTruncatedPoisson)

Creates a new truncated COM-Poisson which is the product of two other truncated COM-Poissons

Declaration

public static LeftTruncatedPoisson operator *(LeftTruncatedPoisson a, LeftTruncatedPoisson b)

Parameters

Type	Name	Description
LeftTruncatedPoisson	a	The first COM-Poisson
LeftTruncatedPoisson	b	The second COM-Poisson

Returns

Type	Description
LeftTruncatedPoisson	Result of the product.

Implements

IDistribution<T>

IDistribution

System.ICloneable

Diffable

SettableToUniform

HasPoint<T>

CanGetLogProb<T>

CanGetMean<MeanType>

Sampleable<T>

SettableToProduct<T>

SettableToProduct<T, U>

SettableToRatio<T>

SettableToRatio<T, U>

SettableToPower<T>

SettableToWeightedSum<T>

SettableTo<T>

SettableToPartialUniform<TDist>

CanGetLogAverageOf<T>

CanGetAverageLog<T>

CanGetLogNormalizer

ICanTruncateLeft<TDomain>