gov.sandia.cognition.statistics.distribution
Class PoissonDistribution

java.lang.Object
  extended by gov.sandia.cognition.util.AbstractCloneableSerializable
      extended by gov.sandia.cognition.statistics.AbstractDistribution<NumberType>
          extended by gov.sandia.cognition.statistics.AbstractClosedFormUnivariateDistribution<Number>
              extended by gov.sandia.cognition.statistics.distribution.PoissonDistribution
All Implemented Interfaces:
Vectorizable, ClosedFormComputableDistribution<Number>, ClosedFormDiscreteUnivariateDistribution<Number>, ClosedFormDistribution<Number>, ClosedFormUnivariateDistribution<Number>, ComputableDistribution<Number>, DiscreteDistribution<Number>, Distribution<Number>, DistributionWithMean<Number>, EstimableDistribution<Number,PoissonDistribution>, UnivariateDistribution<Number>, CloneableSerializable, Serializable, Cloneable
Direct Known Subclasses:
PoissonDistribution.CDF, PoissonDistribution.PMF

@PublicationReference(author="Wikipedia",
                      title="Poisson distribution",
                      type=WebPage,
                      year=2009,
                      url="http://en.wikipedia.org/wiki/Poisson_distribution")
public class PoissonDistribution
extends AbstractClosedFormUnivariateDistribution<Number>
implements ClosedFormDiscreteUnivariateDistribution<Number>, EstimableDistribution<Number,PoissonDistribution>

A Poisson distribution is the limits of what happens when a Bernoulli trial with "rare" events are sampled on a continuous basis and then binned into discrete time intervals. For example, if two people buy a house every day, then what is the probability that ten people buy a house on some day?

Since:
3.0
Author:
Kevin R. Dixon
See Also:
Serialized Form

Nested Class Summary
static class PoissonDistribution.CDF
          CDF of the PoissonDistribution
static class PoissonDistribution.MaximumLikelihoodEstimator
          Creates a PoissonDistribution from data
static class PoissonDistribution.PMF
          PMF of the PoissonDistribution.
static class PoissonDistribution.WeightedMaximumLikelihoodEstimator
          Creates a PoissonDistribution from weighted data.
 
Field Summary
static double DEFAULT_RATE
          Default rate parameter, 1.0.
protected  double rate
          Expected number of occurrences during the integer interval, must be greater than zero.
 
Constructor Summary
PoissonDistribution()
          Creates a new instance of PoissonDistribution
PoissonDistribution(double rate)
          Creates a new instance of PoissonDistribution
PoissonDistribution(PoissonDistribution other)
          Creates a new instance of PoissonDistribution
 
Method Summary
 PoissonDistribution clone()
          This makes public the clone method on the Object class and removes the exception that it throws.
 void convertFromVector(Vector parameters)
          Converts the object from a Vector of parameters.
 Vector convertToVector()
          Converts the object to a vector.
 PoissonDistribution.CDF getCDF()
          Gets the CDF of a scalar distribution.
 IntegerSpan getDomain()
          Returns an object that allows an iteration through the domain (x-axis, independent variable) of the Distribution
 int getDomainSize()
          Gets the size of the domain.
 PoissonDistribution.MaximumLikelihoodEstimator getEstimator()
          Gets an estimator associated with this distribution.
 Integer getMaxSupport()
          Gets the minimum support (domain or input) of the distribution.
 Double getMean()
          Gets the arithmetic mean, or "first central moment" or "expectation", of the distribution.
 Integer getMinSupport()
          Gets the minimum support (domain or input) of the distribution.
 PoissonDistribution.PMF getProbabilityFunction()
          Gets the distribution function associated with this Distribution, either the PDF or PMF.
 double getRate()
          Getter for rate
 double getVariance()
          Gets the variance of the distribution.
 ArrayList<Number> sample(Random random, int numSamples)
          Draws multiple random samples from the distribution.
 void setRate(double rate)
          Setter for rate
 
Methods inherited from class gov.sandia.cognition.statistics.AbstractDistribution
sample
 
Methods inherited from class java.lang.Object
equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 
Methods inherited from interface gov.sandia.cognition.statistics.Distribution
sample
 

Field Detail

DEFAULT_RATE

public static final double DEFAULT_RATE
Default rate parameter, 1.0.

See Also:
Constant Field Values

rate

protected double rate
Expected number of occurrences during the integer interval, must be greater than zero.

Constructor Detail

PoissonDistribution

public PoissonDistribution()
Creates a new instance of PoissonDistribution


PoissonDistribution

public PoissonDistribution(double rate)
Creates a new instance of PoissonDistribution

Parameters:
rate - Expected number of occurrences during the integer interval, must be greater than zero.

PoissonDistribution

public PoissonDistribution(PoissonDistribution other)
Creates a new instance of PoissonDistribution

Parameters:
other - PoissonDistribution to copy.
Method Detail

clone

public PoissonDistribution clone()
Description copied from class: AbstractCloneableSerializable
This makes public the clone method on the Object class and removes the exception that it throws. Its default behavior is to automatically create a clone of the exact type of object that the clone is called on and to copy all primitives but to keep all references, which means it is a shallow copy. Extensions of this class may want to override this method (but call super.clone() to implement a "smart copy". That is, to target the most common use case for creating a copy of the object. Because of the default behavior being a shallow copy, extending classes only need to handle fields that need to have a deeper copy (or those that need to be reset). Some of the methods in ObjectUtil may be helpful in implementing a custom clone method. Note: The contract of this method is that you must use super.clone() as the basis for your implementation.

Specified by:
clone in interface Vectorizable
Specified by:
clone in interface CloneableSerializable
Overrides:
clone in class AbstractClosedFormUnivariateDistribution<Number>
Returns:
A clone of this object.

getMean

public Double getMean()
Description copied from interface: DistributionWithMean
Gets the arithmetic mean, or "first central moment" or "expectation", of the distribution.

Specified by:
getMean in interface DistributionWithMean<Number>
Returns:
Mean of the distribution.

sample

public ArrayList<Number> sample(Random random,
                                int numSamples)
Description copied from interface: Distribution
Draws multiple random samples from the distribution. It is generally more efficient to use this multiple-sample method than multiple calls of the single-sample method. (But not always.)

Specified by:
sample in interface Distribution<Number>
Parameters:
random - Random-number generator to use in order to generate random numbers.
numSamples - Number of samples to draw from the distribution.
Returns:
Samples drawn according to this distribution.

getCDF

public PoissonDistribution.CDF getCDF()
Description copied from interface: UnivariateDistribution
Gets the CDF of a scalar distribution.

Specified by:
getCDF in interface ClosedFormUnivariateDistribution<Number>
Specified by:
getCDF in interface UnivariateDistribution<Number>
Returns:
CDF of the scalar distribution.

convertToVector

public Vector convertToVector()
Description copied from interface: Vectorizable
Converts the object to a vector.

Specified by:
convertToVector in interface Vectorizable
Returns:
The Vector form of the object.

convertFromVector

public void convertFromVector(Vector parameters)
Description copied from interface: Vectorizable
Converts the object from a Vector of parameters.

Specified by:
convertFromVector in interface Vectorizable
Parameters:
parameters - The parameters to incorporate.

getVariance

public double getVariance()
Description copied from interface: UnivariateDistribution
Gets the variance of the distribution. This is sometimes called the second central moment by more pedantic people, which is equivalent to the square of the standard deviation.

Specified by:
getVariance in interface UnivariateDistribution<Number>
Returns:
Variance of the distribution.

getDomain

public IntegerSpan getDomain()
Description copied from interface: DiscreteDistribution
Returns an object that allows an iteration through the domain (x-axis, independent variable) of the Distribution

Specified by:
getDomain in interface DiscreteDistribution<Number>
Returns:
Collection that enumerates each value that the domain can take

getDomainSize

public int getDomainSize()
Description copied from interface: DiscreteDistribution
Gets the size of the domain.

Specified by:
getDomainSize in interface DiscreteDistribution<Number>
Returns:
The size of the domain.

getProbabilityFunction

public PoissonDistribution.PMF getProbabilityFunction()
Description copied from interface: ComputableDistribution
Gets the distribution function associated with this Distribution, either the PDF or PMF.

Specified by:
getProbabilityFunction in interface ComputableDistribution<Number>
Specified by:
getProbabilityFunction in interface DiscreteDistribution<Number>
Returns:
Distribution function associated with this Distribution.

getRate

public double getRate()
Getter for rate

Returns:
Expected number of occurrences during the integer interval, must be greater than zero.

setRate

public void setRate(double rate)
Setter for rate

Parameters:
rate - Expected number of occurrences during the integer interval, must be greater than zero.

getMinSupport

public Integer getMinSupport()
Description copied from interface: UnivariateDistribution
Gets the minimum support (domain or input) of the distribution.

Specified by:
getMinSupport in interface UnivariateDistribution<Number>
Returns:
Minimum support.

getMaxSupport

public Integer getMaxSupport()
Description copied from interface: UnivariateDistribution
Gets the minimum support (domain or input) of the distribution.

Specified by:
getMaxSupport in interface UnivariateDistribution<Number>
Returns:
Minimum support.

getEstimator

public PoissonDistribution.MaximumLikelihoodEstimator getEstimator()
Description copied from interface: EstimableDistribution
Gets an estimator associated with this distribution.

Specified by:
getEstimator in interface EstimableDistribution<Number,PoissonDistribution>
Returns:
A distribution estimator associated for this distribution.