gov.sandia.cognition.statistics.distribution

Class UnivariateGaussian

java.lang.Object

gov.sandia.cognition.util.AbstractCloneableSerializable

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

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

gov.sandia.cognition.statistics.AbstractClosedFormSmoothUnivariateDistribution

gov.sandia.cognition.statistics.distribution.UnivariateGaussian

All Implemented Interfaces:

Vectorizable, ClosedFormComputableDistribution<java.lang.Double>, ClosedFormDistribution<java.lang.Double>, ClosedFormUnivariateDistribution<java.lang.Double>, ComputableDistribution<java.lang.Double>, Distribution<java.lang.Double>, DistributionWithMean<java.lang.Double>, EstimableDistribution<java.lang.Double,UnivariateGaussian>, SmoothUnivariateDistribution, UnivariateDistribution<java.lang.Double>, CloneableSerializable, java.io.Serializable, java.lang.Cloneable

Direct Known Subclasses:

UnivariateGaussian.CDF, UnivariateGaussian.CDF.Inverse, UnivariateGaussian.PDF

@PublicationReference(author="Wikipedia",
                      title="Normal distribution",
                      type=WebPage,
                      year=2009,
                      url="http://en.wikipedia.org/wiki/Normal_distribution")
public class UnivariateGaussian
extends AbstractClosedFormSmoothUnivariateDistribution
implements EstimableDistribution<java.lang.Double,UnivariateGaussian>

This class contains internal classes that implement useful functions based on the Gaussian distribution. Use this class if the underlying distribution has a univariate (scalar) Random Variable. If your distribution is Vector based, then use MultivariateGaussian. However, MultivariateGaussian is a MUCH more computationally intensive class.

Since:

3.0

Author:

Kevin R. Dixon

See Also:

Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	UnivariateGaussian.CDF CDF of the underlying Gaussian.
static class	UnivariateGaussian.ErrorFunction Gaussian Error Function, useful for computing the cumulative distribution function for a Gaussian.
static class	UnivariateGaussian.IncrementalEstimator Implements an incremental estimator for the sufficient statistics for a UnivariateGaussian.
static class	UnivariateGaussian.MaximumLikelihoodEstimator Creates a UnivariateGaussian from data
static class	UnivariateGaussian.PDF PDF of the underlying Gaussian.
static class	UnivariateGaussian.SufficientStatistic Captures the sufficient statistics of a UnivariateGaussian, which are the values to estimate the mean and variance.
static class	UnivariateGaussian.WeightedMaximumLikelihoodEstimator Creates a UnivariateGaussian from weighted data

Field Summary

Fields

Modifier and Type	Field and Description
static double	BIG_Z A big value to input into the Gaussian CDF that will get 1.0 probability, 100.0.
static double	DEFAULT_MEAN Default mean, 0.0.
static double	DEFAULT_VARIANCE Default variance, 1.0.
protected double	mean First central moment (expectation) of the distribution
static double	PI2 PI times 2.0, 6.283185307179586
static double	SQRT2 Square root of 2.0, 0.707...
protected double	variance Second central moment (square of standard deviation) of the distribution

Constructor Summary

Constructors

Constructor and Description
UnivariateGaussian() Creates a new instance of UnivariateGaussian with zero mean and unit variance
UnivariateGaussian(double mean, double variance) Creates a new instance of UnivariateGaussian
UnivariateGaussian(UnivariateGaussian other) Copy constructor

Method Summary

Modifier and Type	Method and Description
UnivariateGaussian	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.
UnivariateGaussian	convolve(UnivariateGaussian other) Convolves this Gaussian with the other Gaussian.
UnivariateGaussian.CDF	getCDF() Gets the CDF of a scalar distribution.
UnivariateGaussian.MaximumLikelihoodEstimator	getEstimator() Gets an estimator associated with this distribution.
java.lang.Double	getMaxSupport() Gets the minimum support (domain or input) of the distribution.
java.lang.Double	getMean() Getter for mean
double	getMeanAsDouble() Gets the mean of the distribution as a double.
java.lang.Double	getMinSupport() Gets the minimum support (domain or input) of the distribution.
UnivariateGaussian.PDF	getProbabilityFunction() Gets the distribution function associated with this Distribution, either the PDF or PMF.
double	getStandardDeviation() Gets the standard deviation, which is the square root of the variance.
double	getVariance() Gets the variance of the distribution.
double	sampleAsDouble(java.util.Random random) Samples a value from this distribution as a double.
void	sampleInto(java.util.Random random, double[] output, int start, int length) Samples values from this distribution as an array of doubles.
void	setMean(double mean) Setter for mean
void	setVariance(double variance) Setter for variance
UnivariateGaussian	times(UnivariateGaussian other) Multiplies this Gaussian with the other Gaussian.
java.lang.String	toString() Returns the string representation of the object.

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

sampleAsDoubles, sampleInto

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

sample, sample

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface gov.sandia.cognition.statistics.Distribution

sample, sample, sampleInto

Field Detail

DEFAULT_MEAN

public static final double DEFAULT_MEAN

Default mean, 0.0.

See Also:

Constant Field Values

DEFAULT_VARIANCE

public static final double DEFAULT_VARIANCE

Default variance, 1.0.

See Also:

Constant Field Values

mean

protected double mean

First central moment (expectation) of the distribution

variance

protected double variance

Second central moment (square of standard deviation) of the distribution

BIG_Z

public static final double BIG_Z

A big value to input into the Gaussian CDF that will get 1.0 probability, 100.0.

See Also:

Constant Field Values

SQRT2

public static final double SQRT2

Square root of 2.0, 0.707...

PI2

public static final double PI2

PI times 2.0, 6.283185307179586

See Also:

Constant Field Values

Constructor Detail

UnivariateGaussian

public UnivariateGaussian()

Creates a new instance of UnivariateGaussian with zero mean and unit variance

UnivariateGaussian

public UnivariateGaussian(double mean,
                          double variance)

Creates a new instance of UnivariateGaussian

Parameters:

mean - First central moment (expectation) of the distribution

variance - Second central moment (square of standard deviation) of the distribution

UnivariateGaussian

public UnivariateGaussian(UnivariateGaussian other)

Copy constructor

Parameters:

other - UnivariateGaussian to copy

Method Detail

clone

public UnivariateGaussian 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.Double>

Returns:

A clone of this object.

getMean

public java.lang.Double getMean()

Getter for mean

Specified by:

getMean in interface DistributionWithMean<java.lang.Double>

Specified by:

getMean in interface SmoothUnivariateDistribution

Overrides:

getMean in class AbstractClosedFormSmoothUnivariateDistribution

Returns:

First central moment (expectation) of the distribution

setMean

public void setMean(double mean)

Setter for mean

Parameters:

mean - First central moment (expectation) 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.Double>

Returns:

The mean as a double.

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.Double>

Returns:

Variance of the distribution.

setVariance

public void setVariance(double variance)

Setter for variance

Parameters:

variance - Second central moment (square of standard deviation) of the distribution

getStandardDeviation

public double getStandardDeviation()

Gets the standard deviation, which is the square root of the variance.

Returns:

The standard deviation.

toString

public java.lang.String toString()

Returns the string representation of the object.

Overrides:

toString in class java.lang.Object

Returns:

String representation of the object.

sampleAsDouble

public double sampleAsDouble(java.util.Random random)

Description copied from interface: SmoothUnivariateDistribution

Samples a value from this distribution as a double. This is a convenience method to potentially avoid boxing.

Specified by:

sampleAsDouble in interface SmoothUnivariateDistribution

Overrides:

sampleAsDouble in class AbstractClosedFormSmoothUnivariateDistribution

Parameters:

random - Random number generator to use.

Returns:

A value sampled from this distribution.

sampleInto

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

Description copied from interface: SmoothUnivariateDistribution

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

Specified by:

sampleInto in interface SmoothUnivariateDistribution

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.

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.

getCDF

public UnivariateGaussian.CDF getCDF()

Description copied from interface: UnivariateDistribution

Gets the CDF of a scalar distribution.

Specified by:

getCDF in interface ClosedFormUnivariateDistribution<java.lang.Double>

Specified by:

getCDF in interface SmoothUnivariateDistribution

Specified by:

getCDF in interface UnivariateDistribution<java.lang.Double>

Returns:

CDF of the scalar distribution.

getProbabilityFunction

public UnivariateGaussian.PDF 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.Double>

Specified by:

getProbabilityFunction in interface SmoothUnivariateDistribution

Returns:

Distribution function associated with this Distribution.

getMinSupport

public java.lang.Double getMinSupport()

Description copied from interface: UnivariateDistribution

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

Specified by:

getMinSupport in interface UnivariateDistribution<java.lang.Double>

Returns:

Minimum support.

getMaxSupport

public java.lang.Double getMaxSupport()

Description copied from interface: UnivariateDistribution

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

Specified by:

getMaxSupport in interface UnivariateDistribution<java.lang.Double>

Returns:

Minimum support.

times

public UnivariateGaussian times(UnivariateGaussian other)

Multiplies this Gaussian with the other Gaussian. This is also equivalent to computing the posterior belief using one of the Gaussians as the prior and one as the conditional likelihood.

Parameters:

other - Other Gaussian to multiply with this.

Returns:

Multiplied Gaussians.

convolve

public UnivariateGaussian convolve(UnivariateGaussian other)

Convolves this Gaussian with the other Gaussian.

Parameters:

other - Other Gaussian to convolve with this.

Returns:

Convolved Gaussians.

getEstimator

public UnivariateGaussian.MaximumLikelihoodEstimator getEstimator()

Description copied from interface: EstimableDistribution

Gets an estimator associated with this distribution.

Specified by:

getEstimator in interface EstimableDistribution<java.lang.Double,UnivariateGaussian>

Returns:

A distribution estimator associated for this distribution.