gov.sandia.cognition.statistics.distribution

Class PoissonDistribution

java.lang.Object

gov.sandia.cognition.util.AbstractCloneableSerializable

gov.sandia.cognition.statistics.AbstractDistribution<NumberType>

gov.sandia.cognition.statistics.AbstractClosedFormUnivariateDistribution<java.lang.Number>

gov.sandia.cognition.statistics.AbstractClosedFormIntegerDistribution

gov.sandia.cognition.statistics.distribution.PoissonDistribution

All Implemented Interfaces:

Vectorizable, ClosedFormComputableDistribution<java.lang.Number>, ClosedFormDiscreteUnivariateDistribution<java.lang.Number>, ClosedFormDistribution<java.lang.Number>, ClosedFormUnivariateDistribution<java.lang.Number>, ComputableDistribution<java.lang.Number>, DiscreteDistribution<java.lang.Number>, Distribution<java.lang.Number>, DistributionWithMean<java.lang.Number>, EstimableDistribution<java.lang.Number,PoissonDistribution>, IntegerDistribution, UnivariateDistribution<java.lang.Number>, CloneableSerializable, java.io.Serializable, java.lang.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 AbstractClosedFormIntegerDistribution
implements ClosedFormDiscreteUnivariateDistribution<java.lang.Number>, EstimableDistribution<java.lang.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

Nested Classes

Modifier and Type	Class and Description
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

Fields

Modifier and Type	Field and Description
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

Constructors

Constructor and Description
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

Modifier and Type	Method and Description
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.
java.lang.Integer	getMaxSupport() Gets the minimum support (domain or input) of the distribution.
java.lang.Double	getMean() Gets the arithmetic mean, or "first central moment" or "expectation", of the distribution.
double	getMeanAsDouble() Gets the mean of the distribution as a double.
java.lang.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.
int	sampleAsInt(java.util.Random random) Draws a single random sample from the distribution as an int.
void	sampleInto(java.util.Random random, int[] output, int start, int length) Samples values from this distribution as an array of ints.
void	sampleInto(java.util.Random random, int sampleCount, java.util.Collection<? super java.lang.Number> output) Draws multiple random samples from the distribution and puts the result into the given collection.
void	setRate(double rate) Setter for rate

Methods inherited from class gov.sandia.cognition.statistics.AbstractClosedFormIntegerDistribution

sampleAsInts

Methods inherited from class gov.sandia.cognition.statistics.AbstractDistribution

sample, 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, 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<java.lang.Number>

Returns:

A clone of this object.

getMean

public java.lang.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<java.lang.Number>

Returns:

Mean of the distribution.

getMeanAsDouble

public double getMeanAsDouble()

Description copied from interface: UnivariateDistribution

Gets the mean of the distribution as a double.

Specified by:

getMeanAsDouble in interface UnivariateDistribution<java.lang.Number>

Returns:

The mean as a double.

sampleInto

public void sampleInto(java.util.Random random,
                       int sampleCount,
                       java.util.Collection<? super java.lang.Number> output)

Description copied from interface: Distribution

Draws multiple random samples from the distribution and puts the result into the given collection.

Specified by:

sampleInto in interface Distribution<java.lang.Number>

Parameters:

random - Random number generator to use.

sampleCount - The number of samples to draw. Cannot be negative.

output - The collection to add the samples into.

sampleAsInt

public int sampleAsInt(java.util.Random random)

Description copied from interface: IntegerDistribution

Draws a single random sample from the distribution as an int.

Specified by:

sampleAsInt in interface IntegerDistribution

Parameters:

random - The random number generator to use.

Returns:

A sample from the distribution.

sampleInto

public void sampleInto(java.util.Random random,
                       int[] output,
                       int start,
                       int length)

Description copied from interface: IntegerDistribution

Samples values from this distribution as an array of ints. This is a convenience method to potentially avoid boxing.

Specified by:

sampleInto in interface IntegerDistribution

Overrides:

sampleInto in class AbstractClosedFormIntegerDistribution

Parameters:

random - Random number generator to use.

output - The array to write the result into. Cannot be null.

start - The offset in the array to start writing at. Cannot be negative.

length - The number of values to sample. Cannot be negative.

getCDF

public PoissonDistribution.CDF getCDF()

Description copied from interface: UnivariateDistribution

Gets the CDF of a scalar distribution.

Specified by:

getCDF in interface ClosedFormUnivariateDistribution<java.lang.Number>

Specified by:

getCDF in interface UnivariateDistribution<java.lang.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<java.lang.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<java.lang.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<java.lang.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<java.lang.Number>

Specified by:

getProbabilityFunction in interface DiscreteDistribution<java.lang.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 java.lang.Integer getMinSupport()

Description copied from interface: UnivariateDistribution

Gets the minimum support (domain or input) of the distribution.

Specified by:

getMinSupport in interface UnivariateDistribution<java.lang.Number>

Returns:

Minimum support.

getMaxSupport

public java.lang.Integer getMaxSupport()

Description copied from interface: UnivariateDistribution

Gets the minimum support (domain or input) of the distribution.

Specified by:

getMaxSupport in interface UnivariateDistribution<java.lang.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<java.lang.Number,PoissonDistribution>

Returns:

A distribution estimator associated for this distribution.