RandomVariables
Class BetaVariable

java.lang.Object
  extended byStatistics.RandomVariable
      extended byRandomVariables.BetaVariable

public class BetaVariable
extends RandomVariable

Beta(alpha,beta) variable.


Constructor Summary
BetaVariable(double alpha, double beta)
          Probability density
f(x)=Gamma(alpha+beta)x^(alpha-1)(1-x)^(beta-1)/ Gamma(alpha)Gamma(beta).
 
Method Summary
 double analyticMean()
          Unconditional mean given by exact formula.
 double analyticVariance()
          Unconditional variance given by exact formula.
 cern.jet.random.Beta getBetaDistribution()
          The underlying cern.jet.random.Beta Beta distribution.
 double getValue(int t)
          A new sample from the distribution of X conditioned on information available at time t.
static void main(java.lang.String[] args)
          Allocates a Beta(0.8,1.2) variable and compares the analytic mean and variance to Monte Carlo mean and variance over a sample of size 100,000.
 
Methods inherited from class Statistics.RandomVariable
analyticCentralMoment, analyticConditionalCentraMoment, analyticConditionalMean, analyticConditionalMoment, analyticConditionalVariance, analyticMoment, basicHistogram, centered_X, conditionalEmpiricalDistribution, conditionalExpectation, conditionalExpectation, conditionalExpectation, conditionalExpectation, conditionalExpectation, conditionalHistogram, conditionalHistogram, conditionalMeanAndStandardDeviation, conditionalMeanAndStandardDeviation, conditionalMeanAndStandardDeviation, conditionalMeanAndStandardDeviation, conditionalMoment, conditionalVariance, cumulativeDistributionFunction, displayConditionalHistogram, displayConditionalHistogram, displayConditionalHistogram, displayConditionalHistogram, displayHistogram, displayHistogram, displayHistogram, displayHistogram, div, empiricalDistribution, expectation, expectation, expectation, expectation, expectation, fillSampleSet, get_empiricalDistributionIsInitialized, get_hasAnalyticCentralMoment, get_hasAnalyticMean, get_hasAnalyticMoment, get_hasAnalyticVariance, get_hasConditionalAnalyticCentralMoment, get_hasConditionalAnalyticMean, get_hasConditionalAnalyticMoment, get_hasConditionalAnalyticVariance, histogram, histogram, initEmpiricalDistribution, meanAndStandardDeviation, meanAndStandardDeviation, meanAndStandardDeviation, meanAndStandardDeviation, minus, mult, plus, quantile, scale, setHasAnalyticMean, setHasAnalyticVariance, variance
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

BetaVariable

public BetaVariable(double alpha,
                    double beta)

Probability density
f(x)=Gamma(alpha+beta)x^(alpha-1)(1-x)^(beta-1)/ Gamma(alpha)Gamma(beta).

Parameters:
alpha - first parameter of the Gamma distribution
beta - second parameter of the Gamma distribution
Method Detail

analyticMean

public double analyticMean()
Description copied from class: RandomVariable

Unconditional mean given by exact formula.

Since in general there are no analytic formulas the default is an error message and program abort. Override this in special cases where analytic formulas do exist.

Overrides:
analyticMean in class RandomVariable

analyticVariance

public double analyticVariance()
Description copied from class: RandomVariable

Unconditional variance given by exact formula.

Since in general there are no analytic formulas the default is an error message and program abort. Override this in special cases where analytic formulas do exist.

Overrides:
analyticVariance in class RandomVariable

getBetaDistribution

public cern.jet.random.Beta getBetaDistribution()
The underlying cern.jet.random.Beta Beta distribution. Much additional functionality. See the javdoc of the colt distribution.


getValue

public double getValue(int t)
Description copied from class: RandomVariable

A new sample from the distribution of X conditioned on information available at time t.

This is the crucial method defining the random variable and information structure.

Specified by:
getValue in class RandomVariable
Parameters:
t - time - ingnored no sense of time defined (no conditioning in this context).

main

public static void main(java.lang.String[] args)
Allocates a Beta(0.8,1.2) variable and compares the analytic mean and variance to Monte Carlo mean and variance over a sample of size 100,000. A smoothed histogram is shown also.