edu.ucla.stat.SOCR.distributions

Class JohnsonSBDistribution

java.lang.Object

edu.ucla.stat.SOCR.core.SOCRValueSettable

edu.ucla.stat.SOCR.core.Distribution

edu.ucla.stat.SOCR.distributions.JohnsonSBDistribution

All Implemented Interfaces:

IValueSettable, Pluginable, java.util.Observer

public class JohnsonSBDistribution
extends Distribution

This class models the Johnson SB (Special Bounded) distribution with specified first 4 parameters (mean, SD, skewness, kurtosis): The Johnson family of distributions (N.L. Johnson, 1949), is a versatile model distribution. It is based on a transformation of the standard normal variable, and includes 4 forms: 1. Unbounded: the set of distributions that go to infinity in both the upper or lower tail. 2. Bounded: the set of distributions that have a fixed boundary on either the upper or lower tail, or both. 3. Log Normal: a border between the Unbounded and Bounded distribution forms. 4. Normal: a special case of the Unbounded form. The flexibility of Johnson family of distributions comes from the choice of form and fitting parameters which allows better fits data. The Johnson family involves a transformation of the raw variable to a Normal variable. This facilitates the estimates of the percentiles of the fitted distribution to be calculated from the Normal distribution percentiles. http://www.qualityamerica.com/knowledgecente/knowctrBest_Fit_Johnson.htm http://www.mathwave.com/articles/johnson_sb_distribution.html

Field Summary

Fields inherited from class edu.ucla.stat.SOCR.core.Distribution

applet, CONTINUOUS, DISCRETE, MAXMGFXVAL, MAXMGFYVAL, MINMGFXVAL, MIXED, name

Constructor Summary

Constructors

Constructor and Description
JohnsonSBDistribution() Default constructor: creates a beta distribution with xi and lambda parameters equal to 1
JohnsonSBDistribution(double _xi, double _lambda, double _gamma, double _delta) This general constructor creates a new JohnsonSBDistribution distribution with specified parameters

Method Summary

Methods

Modifier and Type	Method and Description
double	getCDF(double x) This method computes the cumulative distribution function
double	getDelta() Get delta
double	getDensity(double x) Define the beta getDensity function
double	getGamma() Get gamma
double	getLambda() Get lambda
java.lang.String	getOnlineDescription() This method returns an online description of this distribution.
double[]	getParameters() This method gets the 4 parameters
double	getXi()
void	initialize() used for some subclass to initialize before being used
double	inverseCDF(double probability) Computes the inverse Johnson SB CDF function
void	setDelta(double _delta) This method sets Kurtosis
void	setGamma(double _gamma) This method sets skewness
void	setLambda(double _lambda) This method sets sigma
void	setParameters(double _xi, double _lambda, double _gamma, double _delta) This method sets the parameters, computes the default interval
void	setXi(double _xi) This method sets mean
double	simulate() This method simulates a value from the distribution
void	valueChanged(java.util.Observable o, java.lang.Object arg)

Methods inherited from class edu.ucla.stat.SOCR.core.Distribution

addObserver, betaCDF, comb, factorial, findGFRoot, findRoot, gamma, gammaCDF, getDisplayPane, getDomain, getFailureRate, getGFDerivative, getGFSecondDerivative, getInstance, getLocalHelp, getMaxDensity, getMean, getMean, getMedian, getMGF, getMgfDomain, getName, getPGF, getPGFDomain, getQuantile, getSampleMoment, getSD, getSOCRDistributionFunctors, getSOCRDistributions, getType, getVariance, getVariance, logGamma, paramEstimate, perm, sampleMean, sampleVar, setApplet, setDomain, setDomain, setMGFDomain, setMGFDomain, setMGFParameters, setMGFParameters, setMGFParameters, setMGFParameters, setParameters, setPGFDomain, setPGFDomain, setPGFParameters, setPGFParameters, setPGFParameters, setPGFParameters, update, valueChanged

Methods inherited from class edu.ucla.stat.SOCR.core.SOCRValueSettable

createComponentSetter, createValueSetter, createValueSetter, createValueSetter, createValueSetter, getComponentSetter, getComponentSetters, getValueSetter, getValueSetters

Methods inherited from class java.lang.Object

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

Constructor Detail

JohnsonSBDistribution

public JohnsonSBDistribution(double _xi,
                     double _lambda,
                     double _gamma,
                     double _delta)

This general constructor creates a new JohnsonSBDistribution distribution with specified parameters

Parameters:

xi - = location mean

lambda - = scale SD

gamma - = shape skewness

delta - = shape kurtosis

JohnsonSBDistribution

public JohnsonSBDistribution()

Default constructor: creates a beta distribution with xi and lambda parameters equal to 1

Method Detail

initialize

public void initialize()

Description copied from class: Distribution

used for some subclass to initialize before being used

Overrides:

initialize in class Distribution

valueChanged

public void valueChanged(java.util.Observable o,
                java.lang.Object arg)

Overrides:

valueChanged in class Distribution

setParameters

public void setParameters(double _xi,
                 double _lambda,
                 double _gamma,
                 double _delta)

This method sets the parameters, computes the default interval

Parameters:

_xi - = location

_lambda - = scale

_gamma - = shape

_delta - = shape

getParameters

public double[] getParameters()

This method gets the 4 parameters

getXi

public double getXi()

setXi

public void setXi(double _xi)

This method sets mean

getLambda

public double getLambda()

Get lambda

setLambda

public void setLambda(double _lambda)

This method sets sigma

getGamma

public double getGamma()

Get gamma

setGamma

public void setGamma(double _gamma)

This method sets skewness

getDelta

public double getDelta()

Get delta

setDelta

public void setDelta(double _delta)

This method sets Kurtosis

getDensity

public double getDensity(double x)

Define the beta getDensity function

Specified by:

getDensity in class Distribution

getCDF

public double getCDF(double x)

This method computes the cumulative distribution function

Overrides:

getCDF in class Distribution

Parameters:

x - = value to evaluate the CDF at http://www.mathwave.com/articles/johnson_sb_distribution.html

inverseCDF

public double inverseCDF(double probability)

Computes the inverse Johnson SB CDF function

Overrides:

inverseCDF in class Distribution

Parameters:

probability - - a probability value in [0, 1]

Returns:

the value X for which P(X)==P(x < X) = probability.

simulate

public double simulate()

This method simulates a value from the distribution

Overrides:

simulate in class Distribution

getOnlineDescription

public java.lang.String getOnlineDescription()

This method returns an online description of this distribution.

Overrides:

getOnlineDescription in class Distribution