Package jsl.utilities.distributions

Class MTP

java.lang.Object

jsl.utilities.distributions.Distribution

jsl.utilities.distributions.MTP

All Implemented Interfaces:

ControllableIfc, CDFIfc, DistributionFunctionIfc, DistributionIfc, FirstOrderLossFunctionIfc, InverseCDFIfc, LossFunctionDistributionIfc, MeanIfc, SecondOrderLossFunctionIfc, VarianceIfc, GetNameIfc, IdentityIfc, NewInstanceIfc, ParametersIfc, GetRVariableIfc

public class MTP
extends Distribution
implements LossFunctionDistributionIfc

Represents a Mixed translated Poisson random variable

Nested Class Summary

Nested classes/interfaces inherited from class jsl.utilities.distributions.Distribution

Distribution.RandomControls

Field Summary

Fields

Modifier and Type	Field	Description
protected double	myMean
protected double	myMixProb1
protected double	myMixProb2
protected ShiftedLossFunctionDistribution	SD1
protected ShiftedLossFunctionDistribution	SD2

Fields inherited from class jsl.utilities.distributions.Distribution

myId, myName

Constructor Summary

Constructors

Constructor	Description
MTP()	defaults mixing prob = 0.5, shift = 0.0, rate = 1.0
MTP(double[] parameters)	Constructs an MTP with array of parameters parameters[0] - mixing probability; parameters[1] - shift; parameters[2] - rate;
MTP(double mixProb, double shift, double rate)	Constructs an MTP with mixing probabilities 1-mixProb and mixProb with shifts of shift and shift+1 with rates equal to rate
MTP(double mixProb, double shift, double rate, java.lang.String name)	Constructs an MTP using the supplied parameters

Method Summary

Modifier and Type	Method	Description
double	cdf(double x)	Returns the F(x) = Pr{X <= x} where F represents the cumulative distribution function
double	complementaryCDF(double x)	Computes the complementary cumulative probability distribution function for given value of x
double	firstOrderLossFunction(double x)	Computes the first order loss function for the function for given value of x, G1(x) = E[max(X-x,0)]
double	getMean()	Returns the mean or expected value of a distribution
double[]	getParameters()	Gets the parameters
RVariableIfc	getRandomVariable(RNStreamIfc rng)
double	getVariance()	Returns the variance of the distribution if defined
double	invCDF(double p)	Provides the inverse cumulative distribution function for the distribution While closed form solutions for the inverse cdf may not exist, numerical search methods can be used to solve F(X) = U.
static void	main(java.lang.String[] args)
MTP	newInstance()	Returns a new instance of the random source with the same parameters but an independent generator
double	secondOrderLossFunction(double x)	Computes the 2nd order loss function for the distribution function for given value of x, G2(x) = (1/2)E[max(X-x,0)*max(X-x-1,0)]
void	setParameters(double[] parameters)	Sets the parameters
void	setParameters(double rate, double shift, double mixProbability)
double	thirdOrderLossFunction(double x)

Methods inherited from class jsl.utilities.distributions.Distribution

getControls, getId, getName, getStandardDeviation, inverseContinuousCDFViaBisection, inverseContinuousCDFViaBisection, inverseDiscreteCDFViaSearchUp, setControls, setId, setName, toString

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface jsl.utilities.distributions.CDFIfc

cdf

Methods inherited from interface jsl.utilities.random.rvariable.GetRVariableIfc

getRandomVariable, getRandomVariable

Methods inherited from interface jsl.utilities.distributions.VarianceIfc

getStandardDeviation

Field Detail

myMixProb1

protected double myMixProb1

myMixProb2

protected double myMixProb2

myMean

protected double myMean

SD1

protected ShiftedLossFunctionDistribution SD1

SD2

protected ShiftedLossFunctionDistribution SD2

Constructor Detail

MTP

public MTP()

defaults mixing prob = 0.5, shift = 0.0, rate = 1.0

MTP

public MTP(double mixProb,
           double shift,
           double rate)

Constructs an MTP with mixing probabilities 1-mixProb and mixProb with shifts of shift and shift+1 with rates equal to rate

Parameters:

mixProb - the mixing probability

shift - the shift

rate - the rate

MTP

public MTP(double mixProb,
           double shift,
           double rate,
           java.lang.String name)

Constructs an MTP using the supplied parameters

Parameters:

mixProb - the mixing probability

shift - the shift

rate - the rate

name - an optional name/label

MTP

public MTP(double[] parameters)

Constructs an MTP with array of parameters parameters[0] - mixing probability; parameters[1] - shift; parameters[2] - rate;

Parameters:

parameters - the parameter array

Method Detail

newInstance

public final MTP newInstance()

Returns a new instance of the random source with the same parameters but an independent generator

Specified by:

newInstance in interface NewInstanceIfc

Specified by:

newInstance in class Distribution

Returns:

a new instance with the same parameters

cdf

public double cdf(double x)

Description copied from interface: CDFIfc

Returns the F(x) = Pr{X <= x} where F represents the cumulative distribution function

Specified by:

cdf in interface CDFIfc

Parameters:

x - a double representing the upper limit

Returns:

a double representing the probability

getMean

public double getMean()

Description copied from interface: MeanIfc

Returns the mean or expected value of a distribution

Specified by:

getMean in interface MeanIfc

Returns:

double the mean or expected value for the distribution

getParameters

public double[] getParameters()

Description copied from interface: ParametersIfc

Gets the parameters

Specified by:

getParameters in interface ParametersIfc

Returns:

Returns an array of the parameters

getVariance

public double getVariance()

Description copied from interface: VarianceIfc

Returns the variance of the distribution if defined

Specified by:

getVariance in interface VarianceIfc

Returns:

double the variance of the random variable

invCDF

public double invCDF(double p)

Description copied from interface: InverseCDFIfc

Provides the inverse cumulative distribution function for the distribution While closed form solutions for the inverse cdf may not exist, numerical search methods can be used to solve F(X) = U.

Specified by:

invCDF in interface InverseCDFIfc

Parameters:

p - The probability to be evaluated for the inverse, p must be [0,1] or an IllegalArgumentException is thrown

Returns:

The inverse cdf evaluated at the supplied probability

setParameters

public void setParameters(double[] parameters)

Description copied from interface: ParametersIfc

Sets the parameters

Specified by:

setParameters in interface ParametersIfc

Parameters:

parameters - an array of doubles representing the parameters

complementaryCDF

public double complementaryCDF(double x)

Description copied from interface: CDFIfc

Computes the complementary cumulative probability distribution function for given value of x

Specified by:

complementaryCDF in interface CDFIfc

Parameters:

x - The value to be evaluated

Returns:

The probability, 1-P{X<=x}

firstOrderLossFunction

public double firstOrderLossFunction(double x)

Description copied from interface: FirstOrderLossFunctionIfc

Computes the first order loss function for the function for given value of x, G1(x) = E[max(X-x,0)]

Specified by:

firstOrderLossFunction in interface FirstOrderLossFunctionIfc

Parameters:

x - The value to be evaluated

Returns:

The loss function value, E[max(X-x,0)]

secondOrderLossFunction

public double secondOrderLossFunction(double x)

Description copied from interface: SecondOrderLossFunctionIfc

Computes the 2nd order loss function for the distribution function for given value of x, G2(x) = (1/2)E[max(X-x,0)*max(X-x-1,0)]

Specified by:

secondOrderLossFunction in interface SecondOrderLossFunctionIfc

Parameters:

x - The value to be evaluated

Returns:

The loss function value, (1/2)E[max(X-x,0)*max(X-x-1,0)]

thirdOrderLossFunction

public double thirdOrderLossFunction(double x)

setParameters

public void setParameters(double rate,
                          double shift,
                          double mixProbability)

Parameters:

rate - the rate

shift - the shift

mixProbability - the mixing probability

getRandomVariable

public final RVariableIfc getRandomVariable(RNStreamIfc rng)

Specified by:

getRandomVariable in interface GetRVariableIfc

Overrides:

getRandomVariable in class Distribution

Parameters:

rng - the stream to use

Returns:

a random variable

main

public static void main(java.lang.String[] args)