Package jsl.utilities.distributions

Class PearsonType5

java.lang.Object

jsl.utilities.distributions.Distribution

jsl.utilities.distributions.PearsonType5

All Implemented Interfaces:

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

public class PearsonType5
extends Distribution
implements ContinuousDistributionIfc, InverseCDFIfc, GetRVariableIfc

Represents a Pearson Type V distribution, see Law (2007) Simulation Modeling and Analysis, McGraw-Hill, pg 293 Code contributed by Seda Gumrukcu

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
PearsonType5()	Creates a PearsonType5 distribution shape = 1.0 scale = 1.0
PearsonType5(double[] parameters)	Creates a PearsonType5 distribution parameters[0] = shape parameters[1] = scale
PearsonType5(double shape, double scale)	Creates a PearsonType5 distribution
PearsonType5(double shape, double scale, java.lang.String name)	Creates a PearsonType5 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()	Gets the parameters parameters[0] = shape parameters[1] = scale
RVariableIfc	getRandomVariable(RNStreamIfc rng)
double	getScale()	Gets the scale parameter
double	getShape()	Gets the shape parameter
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.
PearsonType5	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[] parameters)	Sets the parameters parameters[0] = shape parameters[1] = scale
void	setParameters(double shape, double scale)	Sets the shape and scale parameters

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

PearsonType5

public PearsonType5()

Creates a PearsonType5 distribution shape = 1.0 scale = 1.0

PearsonType5

public PearsonType5(double[] parameters)

Creates a PearsonType5 distribution parameters[0] = shape parameters[1] = scale

Parameters:

parameters - the parameter array

PearsonType5

public PearsonType5(double shape,
                    double scale)

Creates a PearsonType5 distribution

Parameters:

shape - must be >0

scale - must be > 0

PearsonType5

public PearsonType5(double shape,
                    double scale,
                    java.lang.String name)

Creates a PearsonType5 distribution

Parameters:

shape - must be >0

scale - must be > 0

name - an optional label/name

Method Detail

newInstance

public final PearsonType5 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

setParameters

public final void setParameters(double shape,
                                double scale)

Sets the shape and scale parameters

Parameters:

shape - must be > 0

scale - must be > 0

getDomain

public final Interval getDomain()

Specified by:

getDomain in interface DomainIfc

getShape

public final double getShape()

Gets the shape parameter

Returns:

the shape parameter

getScale

public final double getScale()

Gets the scale parameter

Returns:

the scale parameter

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:

If shape <= 1.0, returns Double.NaN, otherwise, returns the mean

getParameters

public double[] getParameters()

Gets the parameters parameters[0] = shape parameters[1] = scale

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:

If shape <= 2.0, returns Double.NaN, otherwise returns the variance

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

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:

f(x)

setParameters

public void setParameters(double[] parameters)

Sets the parameters parameters[0] = shape parameters[1] = scale

Specified by:

setParameters in interface ParametersIfc

Parameters:

parameters - the parameter array

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