Package jsl.utilities.distributions

Class PearsonType6

java.lang.Object

jsl.utilities.distributions.Distribution

jsl.utilities.distributions.PearsonType6

All Implemented Interfaces:

ControllableIfc, CDFIfc, ContinuousDistributionIfc, DistributionFunctionIfc, DistributionIfc, DomainIfc, InverseCDFIfc, MeanIfc, PDFIfc, VarianceIfc, GetNameIfc, IdentityIfc, NewInstanceIfc, ParametersIfc, GetRVariableIfc

public class PearsonType6
extends Distribution
implements ContinuousDistributionIfc, InverseCDFIfc, GetRVariableIfc

Represents a Pearson Type VI distribution, see Law (2007) Simulation Modeling and Analysis, McGraw-Hill, pg 294

Code contributed by Nabil Lehlou

Nested Class Summary

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

Distribution.RandomControls

Field Summary

Fields inherited from class jsl.utilities.distributions.Distribution

myId, myName

Constructor Summary

Constructors

Constructor	Description
PearsonType6()	Creates a PearsonTypeVI distribution with alpha1 = 2.0 alpha2 = 3.0 beta = 1.0
PearsonType6(double[] parameters)	Creates a PearsonTypeVI distribution
PearsonType6(double alpha1, double alpha2, double beta)	Creates a PearsonTypeVI distribution
PearsonType6(double alpha1, double alpha2, double beta, java.lang.String name)	Creates a PearsonTypeVI 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
Interval	getDomain()
double	getMean()	Returns the mean or expected value of a distribution
double[]	getParameters()	params[0] = alpha1 params[1] = alpha2 params[2] = beta
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.
PearsonType6	newInstance()	Returns a new instance
double	pdf(double x)	Returns the f(x) where f represents the probability density function for the distribution.
void	setParameters(double[] params)	params[0] = alpha1 params[1] = alpha2 params[2] = beta
void	setParameters(double alpha1, double alpha2, double beta)
void	setScale(double beta)
void	setShapeParameters(double alpha1, double alpha2)

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

Constructor Detail

PearsonType6

public PearsonType6()

Creates a PearsonTypeVI distribution with alpha1 = 2.0 alpha2 = 3.0 beta = 1.0

PearsonType6

public PearsonType6(double alpha1,
                    double alpha2,
                    double beta)

Creates a PearsonTypeVI distribution

Parameters:

alpha1 - shape 1

alpha2 - shape 2

beta - scale

PearsonType6

public PearsonType6(double[] parameters)

Creates a PearsonTypeVI distribution

parameters[0] = alpha1 parameters[1] = alpha2 parameters[2] = beta

Parameters:

parameters - the parameter array

PearsonType6

public PearsonType6(double alpha1,
                    double alpha2,
                    double beta,
                    java.lang.String name)

Creates a PearsonTypeVI distribution

Parameters:

alpha1 - shape 1

alpha2 - shape 2

beta - scale

name - an optional name/label

Method Detail

newInstance

public final PearsonType6 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

getDomain

public final Interval getDomain()

Specified by:

getDomain in interface DomainIfc

setParameters

public final void setParameters(double alpha1,
                                double alpha2,
                                double beta)

Parameters:

alpha1 - shape 1

alpha2 - shape 2

beta - scale

setShapeParameters

public final void setShapeParameters(double alpha1,
                                     double alpha2)

Parameters:

alpha1 - shape 1

alpha2 - shape 2

setScale

public void setScale(double beta)

Parameters:

beta - the scale

setParameters

public void setParameters(double[] params)

params[0] = alpha1 params[1] = alpha2 params[2] = beta

Specified by:

setParameters in interface ParametersIfc

Parameters:

params - the parameter array

getParameters

public double[] getParameters()

params[0] = alpha1 params[1] = alpha2 params[2] = beta

Specified by:

getParameters in interface ParametersIfc

Returns:

the parameter array

pdf

public double pdf(double x)

Description copied from interface: PDFIfc

Returns the f(x) where f represents the probability density function for the distribution. Note this is not a probability.

Specified by:

pdf in interface PDFIfc

Parameters:

x - a double representing the value to be evaluated

Returns:

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

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

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:

Returns the mean or Double.NaN if alpha2 <= 1.0

getVariance

public double getVariance()

Description copied from interface: VarianceIfc

Returns the variance of the distribution if defined

Specified by:

getVariance in interface VarianceIfc

Returns:

Returns the variance or Double.NaN if alpha2 <= 2.0

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