Class GammaFromShapeAndRateOpBase

Provides outgoing messages for GammaFromShapeAndRate(Double, Double), given random arguments to the function.

Inheritance

Object

GammaFromShapeAndRateOpBase

GammaFromShapeAndRateOp

GammaFromShapeAndRateOp_Laplace

GammaFromShapeAndRateOp_Slow

Inherited Members

Object.Equals(Object)

Object.Equals(Object, Object)

Object.GetHashCode()

Object.GetType()

Object.MemberwiseClone()

Object.ReferenceEquals(Object, Object)

Object.ToString()

Namespace: Microsoft.ML.Probabilistic.Factors

Assembly: Microsoft.ML.Probabilistic.dll

Syntax

public class GammaFromShapeAndRateOpBase

Methods

AverageLogFactor(Gamma, Gamma, Gamma)

Evidence message for VMP.

Declaration

[Quality(QualityBand.Experimental)]
public static double AverageLogFactor(Gamma sample, Gamma shape, Gamma rate)

Parameters

Type	Name	Description
Gamma	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	shape	Incoming message from shape. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	rate	Incoming message from rate. Must be a proper distribution. If uniform, the result will be uniform.

Returns

Type	Description
Double	Average of the factor's log-value across the given argument distributions.

Remarks

The formula for the result is sum_(sample,shape,rate) p(sample,shape,rate) log(factor(sample,shape,rate)). Adding up these values across all factors and variables gives the log-evidence estimate for VMP.

Exceptions

Type	Condition
ImproperMessageException	sample is not a proper distribution.
ImproperMessageException	shape is not a proper distribution.
ImproperMessageException	rate is not a proper distribution.

AverageLogFactor(Gamma, Double, Double)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(Gamma sample, double shape, double rate)

Parameters

Type	Name	Description
Gamma	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Double	shape	Constant value for shape.
Double	rate	Constant value for rate.

Returns

Type	Description
Double	Average of the factor's log-value across the given argument distributions.

Remarks

The formula for the result is sum_(sample) p(sample) log(factor(sample,shape,rate)). Adding up these values across all factors and variables gives the log-evidence estimate for VMP.

Exceptions

Type	Condition
ImproperMessageException	sample is not a proper distribution.

AverageLogFactor(Double, Double, Double)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(double sample, double shape, double rate)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Double	shape	Constant value for shape.
Double	rate	Constant value for rate.

Returns

Type	Description
Double	Average of the factor's log-value across the given argument distributions.

Remarks

The formula for the result is log(factor(sample,shape,rate)). Adding up these values across all factors and variables gives the log-evidence estimate for VMP.

CalculateDerivatives(Gamma)

Calculate derivatives of \int G(x;a,b) LogGamma(x) dx wrt (a,b)

Declaration

public static Vector CalculateDerivatives(Gamma q)

Parameters

Type	Name	Description
Gamma	q	The Gamma distribution G(x;a,b).

Returns

Type	Description
Vector	A 2-vector containing derivatives of \int G(x;a,b) LogGamma(x) dx wrt (a,b).

Remarks

Calculates expectations in x=log(s) space using Gauss-Hermite quadrature. For each integral the behaviour as x->0 is subtracted from the integrand before performing quadrature to remove the singularity there.

CalculateDerivativesNaive(Gamma)

Declaration

public static Vector CalculateDerivativesNaive(Gamma q)

Parameters

Type	Name	Description
Gamma	q

Returns

Type	Description
Vector

CalculateDerivativesTrapezoid(Gamma)

Declaration

public static Vector CalculateDerivativesTrapezoid(Gamma q)

Parameters

Type	Name	Description
Gamma	q

Returns

Type	Description
Vector

ELogGamma(Gamma)

Calculates \int G(x;a,b) LogGamma(x) dx

Declaration

public static double ELogGamma(Gamma q)

Parameters

Type	Name	Description
Gamma	q	G(x;a,b)

Returns

Type	Description
Double	\int G(x;a,b) LogGamma(x) dx

LogAverageFactor(Gamma, Gamma)

Evidence message for EP.

Declaration

public static double LogAverageFactor(Gamma sample, Gamma to_sample)

Parameters

Type	Name	Description
Gamma	sample	Incoming message from sample.
Gamma	to_sample	Outgoing message to sample.

Returns

Type	Description
Double	Logarithm of the factor's average value across the given argument distributions.

Remarks

The formula for the result is log(sum_(sample) p(sample) factor(sample,shape,rate)).

LogAverageFactor(Gamma, Gamma, Gamma)

Evidence message for EP.

Declaration

[NotSupported("Expectation Propagation does not support Gamma variables with stochastic shape")]
public static double LogAverageFactor(Gamma sample, Gamma shape, Gamma rate)

Parameters

Type	Name	Description
Gamma	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	shape	Incoming message from shape. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	rate	Incoming message from rate. Must be a proper distribution. If uniform, the result will be uniform.

Returns

Type	Description
Double	Logarithm of the factor's average value across the given argument distributions.

Remarks

The formula for the result is log(sum_(sample,shape,rate) p(sample,shape,rate) factor(sample,shape,rate)).

Exceptions

Type	Condition
ImproperMessageException	sample is not a proper distribution.
ImproperMessageException	shape is not a proper distribution.
ImproperMessageException	rate is not a proper distribution.

LogAverageFactor(Gamma, Gamma, Double)

Evidence message for EP.

Declaration

[NotSupported("Expectation Propagation does not support Gamma variables with stochastic shape")]
public static double LogAverageFactor(Gamma sample, Gamma shape, double rate)

Parameters

Type	Name	Description
Gamma	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	shape	Incoming message from shape. Must be a proper distribution. If uniform, the result will be uniform.
Double	rate	Constant value for rate.

Returns

Type	Description
Double	Logarithm of the factor's average value across the given argument distributions.

Remarks

The formula for the result is log(sum_(sample,shape) p(sample,shape) factor(sample,shape,rate)).

Exceptions

Type	Condition
ImproperMessageException	sample is not a proper distribution.
ImproperMessageException	shape is not a proper distribution.

LogAverageFactor(Gamma, Double, Double)

Evidence message for EP.

Declaration

public static double LogAverageFactor(Gamma sample, double shape, double rate)

Parameters

Type	Name	Description
Gamma	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Double	shape	Constant value for shape.
Double	rate	Constant value for rate.

Returns

Type	Description
Double	Logarithm of the factor's average value across the given argument distributions.

Remarks

The formula for the result is log(sum_(sample) p(sample) factor(sample,shape,rate)).

Exceptions

Type	Condition
ImproperMessageException	sample is not a proper distribution.

LogAverageFactor(Double, Gamma, Gamma)

Evidence message for EP.

Declaration

[NotSupported("Expectation Propagation does not support Gamma variables with stochastic shape")]
public static double LogAverageFactor(double sample, Gamma shape, Gamma rate)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Gamma	shape	Incoming message from shape. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	rate	Incoming message from rate. Must be a proper distribution. If uniform, the result will be uniform.

Returns

Type	Description
Double	Logarithm of the factor's average value across the given argument distributions.

Remarks

The formula for the result is log(sum_(shape,rate) p(shape,rate) factor(sample,shape,rate)).

Exceptions

Type	Condition
ImproperMessageException	shape is not a proper distribution.
ImproperMessageException	rate is not a proper distribution.

LogAverageFactor(Double, Gamma, Double)

Evidence message for EP.

Declaration

[NotSupported("Expectation Propagation does not support Gamma variables with stochastic shape")]
public static double LogAverageFactor(double sample, Gamma shape, double rate)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Gamma	shape	Incoming message from shape. Must be a proper distribution. If uniform, the result will be uniform.
Double	rate	Constant value for rate.

Returns

Type	Description
Double	Logarithm of the factor's average value across the given argument distributions.

Remarks

The formula for the result is log(sum_(shape) p(shape) factor(sample,shape,rate)).

Exceptions

Type	Condition
ImproperMessageException	shape is not a proper distribution.

LogAverageFactor(Double, Double, Gamma)

Evidence message for EP.

Declaration

public static double LogAverageFactor(double sample, double shape, Gamma rate)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Double	shape	Constant value for shape.
Gamma	rate	Incoming message from rate.

Returns

Type	Description
Double	Logarithm of the factor's average value across the given argument distributions.

Remarks

The formula for the result is log(sum_(rate) p(rate) factor(sample,shape,rate)).

LogAverageFactor(Double, Double, Double)

Evidence message for EP.

Declaration

public static double LogAverageFactor(double sample, double shape, double rate)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Double	shape	Constant value for shape.
Double	rate	Constant value for rate.

Returns

Type	Description
Double	Logarithm of the factor's average value across the given argument distributions.

Remarks

The formula for the result is log(factor(sample,shape,rate)).

LogEvidenceRatio(Gamma, Double, Double)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(Gamma sample, double shape, double rate)

Parameters

Type	Name	Description
Gamma	sample	Incoming message from sample.
Double	shape	Constant value for shape.
Double	rate	Constant value for rate.

Returns

Type	Description
Double	Logarithm of the factor's contribution the EP model evidence.

Remarks

The formula for the result is log(sum_(sample) p(sample) factor(sample,shape,rate) / sum_sample p(sample) messageTo(sample)). Adding up these values across all factors and variables gives the log-evidence estimate for EP.

LogEvidenceRatio(Double, Double, Gamma)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(double sample, double shape, Gamma rate)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Double	shape	Constant value for shape.
Gamma	rate	Incoming message from rate.

Returns

Type	Description
Double	Logarithm of the factor's contribution the EP model evidence.

Remarks

The formula for the result is log(sum_(rate) p(rate) factor(sample,shape,rate)). Adding up these values across all factors and variables gives the log-evidence estimate for EP.

LogEvidenceRatio(Double, Double, Double)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(double sample, double shape, double rate)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Double	shape	Constant value for shape.
Double	rate	Constant value for rate.

Returns

Type	Description
Double	Logarithm of the factor's contribution the EP model evidence.

Remarks

The formula for the result is log(factor(sample,shape,rate)). Adding up these values across all factors and variables gives the log-evidence estimate for EP.

RateAverageConditional(Gamma, Gamma)

EP message to rate.

Declaration

[NotSupported("Expectation Propagation does not support Gamma variables with stochastic shape")]
public static Gamma RateAverageConditional(Gamma sample, Gamma shape)

Parameters

Type	Name	Description
Gamma	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	shape	Incoming message from shape. Must be a proper distribution. If uniform, the result will be uniform.

Returns

Type	Description
Gamma	The outgoing EP message to the rate argument.

Remarks

The outgoing message is a distribution matching the moments of rate as the random arguments are varied. The formula is proj[p(rate) sum_(sample,shape) p(sample,shape) factor(sample,shape,rate)]/p(rate).

Exceptions

Type	Condition
ImproperMessageException	sample is not a proper distribution.
ImproperMessageException	shape is not a proper distribution.

RateAverageConditional(Double, Double)

EP message to rate.

Declaration

public static Gamma RateAverageConditional(double sample, double shape)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Double	shape	Constant value for shape.

Returns

Type	Description
Gamma	The outgoing EP message to the rate argument.

Remarks

The outgoing message is the factor viewed as a function of rate conditioned on the given values.

RateAverageLogarithm(Gamma, Gamma)

VMP message to rate.

Declaration

public static Gamma RateAverageLogarithm(Gamma sample, Gamma shape)

Parameters

Type	Name	Description
Gamma	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	shape	Incoming message from shape. Must be a proper distribution. If uniform, the result will be uniform.

Returns

Type	Description
Gamma	The outgoing VMP message to the rate argument.

Remarks

The outgoing message is the exponential of the average log-factor value, where the average is over all arguments except rate. The formula is exp(sum_(sample,shape) p(sample,shape) log(factor(sample,shape,rate))).

Exceptions

Type	Condition
ImproperMessageException	sample is not a proper distribution.
ImproperMessageException	shape is not a proper distribution.

RateAverageLogarithm(Gamma, Double)

VMP message to rate.

Declaration

public static Gamma RateAverageLogarithm(Gamma sample, double shape)

Parameters

Type	Name	Description
Gamma	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Double	shape	Constant value for shape.

Returns

Type	Description
Gamma	The outgoing VMP message to the rate argument.

Remarks

The outgoing message is the exponential of the average log-factor value, where the average is over all arguments except rate. The formula is exp(sum_(sample) p(sample) log(factor(sample,shape,rate))).

Exceptions

Type	Condition
ImproperMessageException	sample is not a proper distribution.

RateAverageLogarithm(Double, Gamma)

VMP message to rate.

Declaration

public static Gamma RateAverageLogarithm(double sample, Gamma shape)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Gamma	shape	Incoming message from shape. Must be a proper distribution. If uniform, the result will be uniform.

Returns

Type	Description
Gamma	The outgoing VMP message to the rate argument.

Remarks

The outgoing message is the exponential of the average log-factor value, where the average is over all arguments except rate. The formula is exp(sum_(shape) p(shape) log(factor(sample,shape,rate))).

Exceptions

Type	Condition
ImproperMessageException	shape is not a proper distribution.

RateAverageLogarithm(Double, Double)

VMP message to rate.

Declaration

public static Gamma RateAverageLogarithm(double sample, double shape)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Double	shape	Constant value for shape.

Returns

Type	Description
Gamma	The outgoing VMP message to the rate argument.

Remarks

The outgoing message is the factor viewed as a function of rate conditioned on the given values.

SampleAverageConditional(Gamma, Gamma)

EP message to sample.

Declaration

[NotSupported("Expectation Propagation does not support Gamma variables with stochastic shape")]
public static Gamma SampleAverageConditional(Gamma shape, Gamma rate)

Parameters

Type	Name	Description
Gamma	shape	Incoming message from shape. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	rate	Incoming message from rate. Must be a proper distribution. If uniform, the result will be uniform.

Returns

Type	Description
Gamma	The outgoing EP message to the sample argument.

Remarks

The outgoing message is a distribution matching the moments of sample as the random arguments are varied. The formula is proj[p(sample) sum_(shape,rate) p(shape,rate) factor(sample,shape,rate)]/p(sample).

Exceptions

Type	Condition
ImproperMessageException	shape is not a proper distribution.
ImproperMessageException	rate is not a proper distribution.

SampleAverageConditional(Gamma, Double)

EP message to sample.

Declaration

[NotSupported("Expectation Propagation does not support Gamma variables with stochastic shape")]
public static Gamma SampleAverageConditional(Gamma shape, double rate)

Parameters

Type	Name	Description
Gamma	shape	Incoming message from shape. Must be a proper distribution. If uniform, the result will be uniform.
Double	rate	Constant value for rate.

Returns

Type	Description
Gamma	The outgoing EP message to the sample argument.

Remarks

The outgoing message is a distribution matching the moments of sample as the random arguments are varied. The formula is proj[p(sample) sum_(shape) p(shape) factor(sample,shape,rate)]/p(sample).

Exceptions

Type	Condition
ImproperMessageException	shape is not a proper distribution.

SampleAverageConditional(Double, Double)

EP message to sample.

Declaration

public static Gamma SampleAverageConditional(double shape, double rate)

Parameters

Type	Name	Description
Double	shape	Constant value for shape.
Double	rate	Constant value for rate.

Returns

Type	Description
Gamma	The outgoing EP message to the sample argument.

Remarks

The outgoing message is the factor viewed as a function of sample conditioned on the given values.

SampleAverageConditionalInit()

Declaration

public static Gamma SampleAverageConditionalInit()

Returns

Type	Description
Gamma

Remarks

SampleAverageLogarithm(Gamma, Gamma)

VMP message to sample.

Declaration

[Quality(QualityBand.Experimental)]
public static Gamma SampleAverageLogarithm(Gamma shape, Gamma rate)

Parameters

Type	Name	Description
Gamma	shape	Incoming message from shape. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	rate	Incoming message from rate. Must be a proper distribution. If uniform, the result will be uniform.

Returns

Type	Description
Gamma	The outgoing VMP message to the sample argument.

Remarks

The outgoing message is the exponential of the average log-factor value, where the average is over all arguments except sample. The formula is exp(sum_(shape,rate) p(shape,rate) log(factor(sample,shape,rate))).

Exceptions

Type	Condition
ImproperMessageException	shape is not a proper distribution.
ImproperMessageException	rate is not a proper distribution.

SampleAverageLogarithm(Gamma, Double)

VMP message to sample.

Declaration

[Quality(QualityBand.Experimental)]
public static Gamma SampleAverageLogarithm(Gamma shape, double rate)

Parameters

Type	Name	Description
Gamma	shape	Incoming message from shape. Must be a proper distribution. If uniform, the result will be uniform.
Double	rate	Constant value for rate.

Returns

Type	Description
Gamma	The outgoing VMP message to the sample argument.

Remarks

The outgoing message is the exponential of the average log-factor value, where the average is over all arguments except sample. The formula is exp(sum_(shape) p(shape) log(factor(sample,shape,rate))).

Exceptions

Type	Condition
ImproperMessageException	shape is not a proper distribution.

SampleAverageLogarithm(Double, Gamma)

VMP message to sample.

Declaration

public static Gamma SampleAverageLogarithm(double shape, Gamma rate)

Parameters

Type	Name	Description
Double	shape	Constant value for shape.
Gamma	rate	Incoming message from rate. Must be a proper distribution. If uniform, the result will be uniform.

Returns

Type	Description
Gamma	The outgoing VMP message to the sample argument.

Remarks

The outgoing message is the exponential of the average log-factor value, where the average is over all arguments except sample. The formula is exp(sum_(rate) p(rate) log(factor(sample,shape,rate))).

Exceptions

Type	Condition
ImproperMessageException	rate is not a proper distribution.

SampleAverageLogarithm(Double, Double)

VMP message to sample.

Declaration

public static Gamma SampleAverageLogarithm(double shape, double rate)

Parameters

Type	Name	Description
Double	shape	Constant value for shape.
Double	rate	Constant value for rate.

Returns

Type	Description
Gamma	The outgoing VMP message to the sample argument.

Remarks

The outgoing message is the factor viewed as a function of sample conditioned on the given values.

ShapeAverageConditional(Gamma, Gamma, Gamma, Gamma)

EP message to shape.

Declaration

[NotSupported("Expectation Propagation does not support Gamma variables with stochastic shape")]
public static Gamma ShapeAverageConditional(Gamma sample, Gamma shape, Gamma rate, Gamma result)

Parameters

Type	Name	Description
Gamma	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	shape	Incoming message from shape. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	rate	Incoming message from rate. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	result	Modified to contain the outgoing message.

Returns

Type	Description
Gamma	result

Remarks

The outgoing message is a distribution matching the moments of shape as the random arguments are varied. The formula is proj[p(shape) sum_(sample,rate) p(sample,rate) factor(sample,shape,rate)]/p(shape).

Exceptions

Type	Condition
ImproperMessageException	sample is not a proper distribution.
ImproperMessageException	shape is not a proper distribution.
ImproperMessageException	rate is not a proper distribution.

ShapeAverageConditional(Gamma, Gamma, Double, Gamma)

EP message to shape.

Declaration

[NotSupported("Expectation Propagation does not support Gamma variables with stochastic shape")]
public static Gamma ShapeAverageConditional(Gamma sample, Gamma shape, double rate, Gamma result)

Parameters

Type	Name	Description
Gamma	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	shape	Incoming message from shape. Must be a proper distribution. If uniform, the result will be uniform.
Double	rate	Constant value for rate.
Gamma	result	Modified to contain the outgoing message.

Returns

Type	Description
Gamma	result

Remarks

The outgoing message is a distribution matching the moments of shape as the random arguments are varied. The formula is proj[p(shape) sum_(sample) p(sample) factor(sample,shape,rate)]/p(shape).

Exceptions

Type	Condition
ImproperMessageException	sample is not a proper distribution.
ImproperMessageException	shape is not a proper distribution.

ShapeAverageConditional(Double, Gamma, Gamma, Gamma)

EP message to shape.

Declaration

[NotSupported("Expectation Propagation does not support Gamma variables with stochastic shape")]
public static Gamma ShapeAverageConditional(double sample, Gamma shape, Gamma rate, Gamma result)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Gamma	shape	Incoming message from shape. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	rate	Incoming message from rate. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	result	Modified to contain the outgoing message.

Returns

Type	Description
Gamma	result

Remarks

The outgoing message is a distribution matching the moments of shape as the random arguments are varied. The formula is proj[p(shape) sum_(rate) p(rate) factor(sample,shape,rate)]/p(shape).

Exceptions

Type	Condition
ImproperMessageException	shape is not a proper distribution.
ImproperMessageException	rate is not a proper distribution.

ShapeAverageConditional(Double, Gamma, Double, Gamma)

EP message to shape.

Declaration

[NotSupported("Expectation Propagation does not support Gamma variables with stochastic shape")]
public static Gamma ShapeAverageConditional(double sample, Gamma shape, double rate, Gamma result)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Gamma	shape	Incoming message from shape. Must be a proper distribution. If uniform, the result will be uniform.
Double	rate	Constant value for rate.
Gamma	result	Modified to contain the outgoing message.

Returns

Type	Description
Gamma	result

Remarks

The outgoing message is the factor viewed as a function of shape conditioned on the given values.

Exceptions

Type	Condition
ImproperMessageException	shape is not a proper distribution.

ShapeAverageLogarithm(Gamma, Gamma, Gamma, Gamma)

VMP message to shape.

Declaration

[Quality(QualityBand.Experimental)]
public static Gamma ShapeAverageLogarithm(Gamma sample, Gamma shape, Gamma rate, Gamma to_shape)

Parameters

Type	Name	Description
Gamma	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	shape	Incoming message from shape. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	rate	Incoming message from rate. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	to_shape	Previous outgoing message to shape.

Returns

Type	Description
Gamma	The outgoing VMP message to the shape argument.

Remarks

The outgoing message is the exponential of the average log-factor value, where the average is over all arguments except shape. The formula is exp(sum_(sample,rate) p(sample,rate) log(factor(sample,shape,rate))).

Exceptions

Type	Condition
ImproperMessageException	sample is not a proper distribution.
ImproperMessageException	shape is not a proper distribution.
ImproperMessageException	rate is not a proper distribution.