edu.ucla.stat.SOCR.distributions
Class MultiNomialDistribution

java.lang.Object
  edu.ucla.stat.SOCR.core.SOCRValueSettable
      edu.ucla.stat.SOCR.core.Distribution
          edu.ucla.stat.SOCR.distributions.MultiNomialDistribution

All Implemented Interfaces:

IValueSettable, Pluginable, java.awt.event.ActionListener, java.util.EventListener, java.util.Observer

public class MultiNomialDistribution
extends Distribution
implements java.awt.event.ActionListener

The Multinomial distribution with parameter-vector (k,p), where n=number of trials and event-probabilities p=(p1, p2, ..., pn), with sum(p_k)=1 and p_k>=0, 1<=k<=n. http://en.wikipedia.org/wiki/Multinomial_distribution is a generalization of the binomial distribution.

Field Summary

protected int	k
protected int	n
protected double[]	p
int	type
protected int[]	x

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

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

Constructor Summary

MultiNomialDistribution()
This default constructor creates a new MultiNomialDistribution(2, {0.5, 0.5})

MultiNomialDistribution(int n, double[] p, int[] x)
This general constructor creates a new MultiNomialDistribution with specified parameters:

Method Summary

void	actionPerformed(java.awt.event.ActionEvent e) This method handles the events associated with the changing the Multinomial probabilities or x-values.
double	getCDF(int[] x)
static double	getCDF(int n, double[] p, int[] x) http://controls.engin.umich.edu/wiki/index.php/Multinomial_distributions
double[][]	getCorrelation()
static double[][]	getCorrelation(int n, double[] p)
double[][]	getCovariance() This method returns the variance-covariance matrix of the Multinomail distribution, which is defined as sigma(i,j) = E[(Xi - mu(i))(Xj - mu(j))].
static double[][]	getCovariance(int n, double[] p)
double	getDensity(double x) Define the Multinomial getDensity function
double	getDensity(int[] x) This method computes the density function of the Multinomail distribution
static double[]	getMean(int n, double[] p)
static double[]	getMLE(int[][] x, int m, int d, int n) This method returns the array of MLE estimates for the Mulinomial Probabilities.
java.lang.String	getMultiNomialTestResults() This method returns a Text Array with All cumulative Multinomial results
int	getN()
java.lang.String	getOnlineDescription() This method returns an online description of this distribution.
double[]	getP()
double[]	getProbabilities() This method gets the array of Multinomail parameters (probabilities[]).
double	getProbability(int[] x)
static double	getProbability(int n, double[] p, int[] x) This method computes the density function of the Multinomail distribution
int[]	getXvalues() This method gets the array of Multinomail parameters (x-Values[]).
int	getXvaluesSum() This method gets the array of Multinomail parameters (x-Values[]).
void	initialize() used for some subclass to initialize before being used
void	setParameters(int n, double[] p, int[] x)
void	valueChanged()

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

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

Field Detail

k

protected int k

n

protected int n

p

protected double[] p

x

protected int[] x

type

public int type

Constructor Detail

MultiNomialDistribution

public MultiNomialDistribution(int n,
                               double[] p,
                               int[] x)

This general constructor creates a new MultiNomialDistribution with specified parameters:

Parameters:

n - Total Sum of X-values (Frequencies)

p - array of Probabilities/likelihoods of all outcomes

MultiNomialDistribution

public MultiNomialDistribution()

This default constructor creates a new MultiNomialDistribution(2, {0.5, 0.5})

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()

Overrides:

valueChanged in class Distribution

actionPerformed

public void actionPerformed(java.awt.event.ActionEvent e)

This method handles the events associated with the changing the Multinomial probabilities or x-values.

Specified by:

actionPerformed in interface java.awt.event.ActionListener

Parameters:

e - the action event

getProbabilities

public double[] getProbabilities()

This method gets the array of Multinomail parameters (probabilities[]).

Parameters:

probabilities - the array of the probailities of the Multinomial Distributions

getXvalues

public int[] getXvalues()

This method gets the array of Multinomail parameters (x-Values[]).

Returns:

xValues the array of the X-values of the Multinomial Distributions

getXvaluesSum

public int getXvaluesSum()

This method gets the array of Multinomail parameters (x-Values[]).

Returns:

xValuesSum the Sum of the array of the X-values of the Multinomial Distributions

getProbability

public double getProbability(int[] x)

getDensity

public double getDensity(double x)

Define the Multinomial getDensity function

Specified by:

getDensity in class Distribution

getN

public int getN()

getP

public double[] getP()

getCDF

public double getCDF(int[] x)

getCovariance

public double[][] getCovariance()

This method returns the variance-covariance matrix of the Multinomail distribution, which is defined as sigma(i,j) = E[(Xi - mu(i))(Xj - mu(j))].

Returns:

VarianceMatrix variance-covariance matrix of the Multinomial Distributions

getCorrelation

public double[][] getCorrelation()

getDensity

public double getDensity(int[] x)

This method computes the density function of the Multinomail distribution

Parameters:

x - a vector of outcomes i

Returns:

the probability density of the vector x

getProbability

public static double getProbability(int n,
                                    double[] p,
                                    int[] x)

This method computes the density function of the Multinomail distribution

Parameters:

n - Total sum ov x-values vector (total frequencies

p - multinomial probabilities

x - X-values (frequency) vector

Returns:

CDF CDF value

getCDF

public static double getCDF(int n,
                            double[] p,
                            int[] x)

http://controls.engin.umich.edu/wiki/index.php/Multinomial_distributions

Parameters:

n - total sum of the x-value (frequency) vector

p - Multinomial Probabilities

x - X-values (frequencies)

Returns:

CDF CDF value

getMean

public static double[] getMean(int n,
                               double[] p)

getCovariance

public static double[][] getCovariance(int n,
                                       double[] p)

getCorrelation

public static double[][] getCorrelation(int n,
                                        double[] p)

getMultiNomialTestResults

public java.lang.String getMultiNomialTestResults()

This method returns a Text Array with All cumulative Multinomial results

getMLE

public static double[] getMLE(int[][] x,
                              int m,
                              int d,
                              int n)

This method returns the array of MLE estimates for the Mulinomial Probabilities.

Parameters:

x - double array of X-values -- list of observations used to evaluate prob-parameters

m - the number of observations used to evaluate parameters

d - the dimension of each observation

n - the number of independent trials for each series

Returns:

probabilities the array of the probailities of the Multinomial Distributions (P-hat vector)

setParameters

public void setParameters(int n,
                          double[] p,
                          int[] x)

getOnlineDescription

public java.lang.String getOnlineDescription()

This method returns an online description of this distribution.

Overrides:

getOnlineDescription in class Distribution