Package jsl.utilities.distributions

Class ShiftedDistribution

java.lang.Object

jsl.utilities.distributions.Distribution

jsl.utilities.distributions.ShiftedDistribution

All Implemented Interfaces:

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

Direct Known Subclasses:

ShiftedLossFunctionDistribution

public class ShiftedDistribution
extends Distribution
implements LossFunctionDistributionIfc

Represents a Distribution that has been Shifted (translated to the right) The shift must be >= 0.0

Nested Class Summary

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

Distribution.RandomControls

Field Summary

Fields

Modifier and Type	Field	Description
protected DistributionIfc	myDistribution
protected LossFunctionDistributionIfc	myLossFunctionDistribution
protected double	myShift

Fields inherited from class jsl.utilities.distributions.Distribution

myId, myName

Constructor Summary

Constructors

Constructor	Description
ShiftedDistribution(DistributionIfc distribution, double shift)	Constructs a shifted distribution based on the provided distribution
ShiftedDistribution(DistributionIfc distribution, double shift, java.lang.String name)	Constructs a shifted distribution based on t he provided distribution

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	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 for the shifted distribution shift = parameter[0] The other elements of the returned array are the parameters of the underlying distribution
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.
ShiftedDistribution	newInstance()	Returns a new instance
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	setDistribution(DistributionIfc distribution, double shift)	Changes the underlying distribution and the shift
void	setParameters(double[] parameters)	Sets the parameters of the shifted distribution shift = parameter[0] If supplied, the other elements of the array are used in setting the parameters of the underlying distribution.
void	setShift(double shift)	Changes the shift
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, complementaryCDF

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

getRandomVariable, getRandomVariable

Methods inherited from interface jsl.utilities.distributions.VarianceIfc

getStandardDeviation

Field Detail

myDistribution

protected DistributionIfc myDistribution

myLossFunctionDistribution

protected LossFunctionDistributionIfc myLossFunctionDistribution

myShift

protected double myShift

Constructor Detail

ShiftedDistribution

public ShiftedDistribution(DistributionIfc distribution,
                           double shift)

Constructs a shifted distribution based on the provided distribution

Parameters:

distribution - the distribution to shift

shift - The linear shift

ShiftedDistribution

public ShiftedDistribution(DistributionIfc distribution,
                           double shift,
                           java.lang.String name)

Constructs a shifted distribution based on t he provided distribution

Parameters:

distribution - the distribution to shift

shift - The linear shift

name - an optional name/label

Method Detail

newInstance

public final ShiftedDistribution newInstance()

Description copied from interface: NewInstanceIfc

Returns a new instance

Specified by:

newInstance in interface NewInstanceIfc

Specified by:

newInstance in class Distribution

Returns:

the new instance

setDistribution

public final void setDistribution(DistributionIfc distribution,
                                  double shift)

Changes the underlying distribution and the shift

Parameters:

distribution - must not be null

shift - must be >=0.0

setShift

public final void setShift(double shift)

Changes the shift

Parameters:

shift - must be >=0.0

setParameters

public final void setParameters(double[] parameters)

Sets the parameters of the shifted distribution shift = parameter[0] If supplied, the other elements of the array are used in setting the parameters of the underlying distribution. If only the shift is supplied as a parameter, then the underlying distribution's parameters are not changed (and do not need to be supplied)

Specified by:

setParameters in interface ParametersIfc

Parameters:

parameters - an array of doubles representing the parameters

cdf

public final 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 final 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 final double[] getParameters()

Gets the parameters for the shifted distribution shift = parameter[0] The other elements of the returned array are the parameters of the underlying distribution

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

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)

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