edu.ucla.stat.SOCR.distributions

Class DiscreteArcsineDistribution

java.lang.Object

edu.ucla.stat.SOCR.core.SOCRValueSettable

edu.ucla.stat.SOCR.core.Distribution

edu.ucla.stat.SOCR.distributions.DiscreteArcsineDistribution

All Implemented Interfaces:

IValueSettable, Pluginable, java.util.Observer

public class DiscreteArcsineDistribution
extends Distribution

This class models the discrete ArcSine distribution that governs the last zero in a symmetric random walk on an interval. http://www.math.uu.nl/people/gnedin/ArcSin.ps Example: for 20 tosses with probability about 0.35 one of the players will never be in the winning zone. And the chance of parity 10:10 is only 0.06. The probability law p_{2k,2n}=\choose{2k,k} \times \choose{2n-2k, n-k} \times 2^{-2n}, for all k=0, 1, ..., n is the discrete arcsine's distribution for the time spent in the winning zone.

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
DiscreteArcsineDistribution() This default constructor creates a new discrete arcsine distribution with 10 steps.
DiscreteArcsineDistribution(int n) This general constructor creates a new discrete arcsine distribution with a specified number of steps.

Method Summary

Methods

Modifier and Type	Method and Description
double	getDensity(double x) This method computes the density function.
double	getMaxDensity() This method computes the maximum value of the density function.
java.lang.String	getOnlineDescription() This method returns an online description of this distribution.
int	getParameter() This method gets the parameter, the number of steps.
void	initialize() used for some subclass to initialize before being used
void	setParameter(int n) This method sets the parameter, the number of steps.
double	simulate() This method simulates a value from the distribution, by simulating a random walk on the interval.
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, 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, 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

DiscreteArcsineDistribution

public DiscreteArcsineDistribution(int n)

This general constructor creates a new discrete arcsine distribution with a specified number of steps.

DiscreteArcsineDistribution

public DiscreteArcsineDistribution()

This default constructor creates a new discrete arcsine distribution with 10 steps.

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

setParameter

public void setParameter(int n)

This method sets the parameter, the number of steps.

getDensity

public double getDensity(double x)

This method computes the density function.

Specified by:

getDensity in class Distribution

getMaxDensity

public double getMaxDensity()

This method computes the maximum value of the density function.

Overrides:

getMaxDensity in class Distribution

getParameter

public int getParameter()

This method gets the parameter, the number of steps.

simulate

public double simulate()

This method simulates a value from the distribution, by simulating a random walk on the interval.

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