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

Constructors

TruncatedPoisson()

Initializes a new instance of the TruncatedPoisson class.

Declaration

public TruncatedPoisson()

TruncatedPoisson(LeftTruncatedPoisson)

Initializes a new instance of the TruncatedPoisson class.

Declaration

public TruncatedPoisson(LeftTruncatedPoisson truncatedDistribution)

Parameters

Type	Name	Description
LeftTruncatedPoisson	truncatedDistribution	The underlying left-truncated CoM-Poisson distribution.

TruncatedPoisson(LeftTruncatedPoisson, Int32)

Initializes a new instance of the TruncatedPoisson class.

Declaration

public TruncatedPoisson(LeftTruncatedPoisson leftTruncatedDistribution, int endPoint)

Parameters

Type	Name	Description
LeftTruncatedPoisson	leftTruncatedDistribution	The underlying left-truncated CoM-Poisson distribution.
Int32	endPoint	The index of the last non-zero term in the truncated distribution.

TruncatedPoisson(Poisson, Int32)

Initializes a new instance of the TruncatedPoisson class.

Declaration

public TruncatedPoisson(Poisson nonTruncatedDistribution, int startPoint)

Parameters

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

TruncatedPoisson(Poisson, Int32, Int32)

Initializes a new instance of the TruncatedPoisson class.

Declaration

public TruncatedPoisson(Poisson nonTruncatedDistribution, int startPoint, int endPoint)

Parameters

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

TruncatedPoisson(Double, Double, Int32)

Initializes a new instance of the TruncatedPoisson class.

Declaration

public TruncatedPoisson(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.

TruncatedPoisson(Double, Double, Int32, Int32)

Initializes a new instance of the TruncatedPoisson class.

Declaration

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

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.
Int32	endPoint	The index of the last non-zero term in the truncated distribution.

TruncatedPoisson(Double, Int32)

Initializes a new instance of the TruncatedPoisson class.

Declaration

public TruncatedPoisson(double rate, int startPoint)

Parameters

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

Fields

PositiveInfinityEndPoint

Declaration

public const int PositiveInfinityEndPoint = 2147483647

Field Value

Type	Description
Int32

Properties

EndPoint

The last non-zero point.

Declaration

[DataMember]
public int EndPoint { get; }

Property Value

Type	Description
Int32

EndPointIsPositiveInfinity

Gets a value indicating whether the current distribution is right-truncated.

Declaration

public bool EndPointIsPositiveInfinity { get; }

Property Value

Type	Description
Boolean

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

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

public int StartPoint { get; }

Property Value

Type	Description
Int32

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 TruncatedPoisson struct given a target mean, a start point and a end point.

Declaration

public static TruncatedPoisson 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
TruncatedPoisson	A new instance with the target mean.

FromMeanAndStartPointAndEndPoint(Double, Double, Int32, Int32, Double, Int32)

Initializes a new instance of the TruncatedPoisson struct given a target mean, a start point and a end point.

Declaration

public static TruncatedPoisson FromMeanAndStartPointAndEndPoint(double targetMean, double precision, int startPoint, int endPoint, 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.
Int32	endPoint	The end point.
Double	tolerance	Tolerance for mean.
Int32	maxIterations	Maximum iterations for binary search.

Returns

Type	Description
TruncatedPoisson	A new instance with the target mean.

GetAverageLog(TruncatedPoisson)

The expected logarithm of that distribution under this distribution.

Declaration

public double GetAverageLog(TruncatedPoisson that)

Parameters

Type	Name	Description
TruncatedPoisson	that

Returns

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

Remarks

This is also known as the cross entropy.

GetEndPoint()

Gets the end point of the truncated distribution.

Declaration

public int GetEndPoint()

Returns

Type	Description
Int32	The end point.

GetLogAverageOf(TruncatedPoisson)

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

Declaration

public double GetLogAverageOf(TruncatedPoisson that)

Parameters

Type	Name	Description
TruncatedPoisson	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, Int32)

Gets the log normalizer of a truncated Poisson.

Declaration

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

Parameters

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

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.

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.

PartialUniform(Int32)

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

Declaration

public static TruncatedPoisson PartialUniform(int startPoint)

Parameters

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

Returns

Type	Description
TruncatedPoisson	A new uniform truncated Com-Poisson distribution

PartialUniform(Int32, Int32)

Instantiates a uniform truncated Com-Poisson distribution between given start and end points.

Declaration

public static TruncatedPoisson PartialUniform(int startPoint, int endPoint)

Parameters

Type	Name	Description
Int32	startPoint	The index of the first non-zero term in the truncated distribution.
Int32	endPoint	The index of the last non-zero term in the truncated distribution.

Returns

Type	Description
TruncatedPoisson	A new uniform truncated Com-Poisson distribution

PointMass(Int32)

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

Declaration

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

Parameters

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

Returns

Type	Description
TruncatedPoisson	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

SetTo(TruncatedPoisson)

Set the instance to have the same value as given

Declaration

public void SetTo(TruncatedPoisson value)

Parameters

Type	Name	Description
TruncatedPoisson	value

SetToPartialUniform()

Sets the distribution to be uniform over its support.

Declaration

public void SetToPartialUniform()

SetToPartialUniform(Int32, Int32)

Sets the current distribution to be uniform between given start and end points.

Declaration

public void SetToPartialUniform(int startPoint, int endPoint)

Parameters

Type	Name	Description
Int32	startPoint	The index of the first non-zero term in the truncated distribution.
Int32	endPoint	The index of the last non-zero term in the truncated distribution.

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(TruncatedPoisson)

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

Declaration

public void SetToPartialUniformOf(TruncatedPoisson dist)

Parameters

Type	Name	Description
TruncatedPoisson	dist

SetToProduct(TruncatedPoisson, TruncatedPoisson)

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

Declaration

public void SetToProduct(TruncatedPoisson a, TruncatedPoisson b)

Parameters

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

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()

TruncateLeft(Int32)

Truncates the distribution at the given point.

Declaration

public void TruncateLeft(int startPoint)

Parameters

Type	Name	Description
Int32	startPoint

TruncateRight(Int32)

Truncates the distribution at the given point.

Declaration

public void TruncateRight(int endPoint)

Parameters

Type	Name	Description
Int32	endPoint

Uniform()

Instantiates a uniform truncated Com-Poisson distribution

Declaration

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

Returns

Type	Description
TruncatedPoisson	A new uniform Com-Poisson distribution

Implements

IDistribution<T>

IDistribution

System.ICloneable

Diffable

SettableToUniform

HasPoint<T>

CanGetLogProb<T>

CanGetMean<MeanType>

Sampleable<T>

SettableToProduct<T>

SettableToProduct<T, U>

SettableTo<T>

SettableToPartialUniform<TDist>

CanGetLogAverageOf<T>

CanGetAverageLog<T>

CanGetLogNormalizer

ICanTruncateLeft<TDomain>

ICanTruncateRight<TDomain>