RandomVariables
Class PoissonVariable

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

public class PoissonVariable
extends RandomVariable

Poisson variable, the only parameter is the mean.


Constructor Summary
PoissonVariable(double mean)
           
 
Method Summary
 double analyticMean()
          Unconditional mean given by exact formula.
 double analyticVariance()
          Unconditional variance given by exact formula.
 cern.jet.random.Poisson getPoissonDistribution()
          The underlying cern.jet.random.Poisson 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 Poisson(3) 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

PoissonVariable

public PoissonVariable(double mean)
Parameters:
mean - mean of the 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

getPoissonDistribution

public cern.jet.random.Poisson getPoissonDistribution()

The underlying cern.jet.random.Poisson distribution. Much additional functionality. See the javdoc of the colt distribution.

WARNING: histogram is smoothed, smooths out the discrete nature of the 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 Poisson(3) variable and compares the analytic mean and variance to Monte Carlo mean and variance over a sample of size 100,000. A histogram is shown also.