gov.sandia.cognition.statistics.distribution

Class ParetoDistribution

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.ParetoDistribution

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>, SmoothUnivariateDistribution, UnivariateDistribution<java.lang.Double>, CloneableSerializable, java.io.Serializable, java.lang.Cloneable

Direct Known Subclasses:

ParetoDistribution.CDF, ParetoDistribution.PDF

@PublicationReference(author="Wikipedia",
                      title="Normal distribution",
                      type=WebPage,
                      year=2010,
                      url="http://en.wikipedia.org/wiki/Pareto_distribution")
public class ParetoDistribution
extends AbstractClosedFormSmoothUnivariateDistribution

This class describes the Pareto distribution, sometimes called the Bradford Distribution. The Pareto distribution tends to be used to model social phenomena, such as the distribution of wealth in a society, price returns of stocks, file sizes on a computer, etc. It encapsulates the notion that there are few large entities and many smaller ones (80 percent of the wealth is controlled by 20 percent of the population).

Since:

3.0

Author:

Kevin R. Dixon

See Also:

Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	ParetoDistribution.CDF CDF of the Pareto Distribution.
static class	ParetoDistribution.PDF PDF of the ParetoDistribution

Field Summary

Fields

Modifier and Type	Field and Description
static double	DEFALUT_SCALE Default scale, 1.0.
static double	DEFAULT_SHAPE Default shape, 2.0.
static double	DEFAULT_SHIFT Default shift, 0.0.
protected double	scale Scale parameter, must be greater than zero.
protected double	shape Scale parameter, must be greater than zero.
protected double	shift Amount to shift the distribution to the left.

Constructor Summary

Constructors

Constructor and Description
ParetoDistribution() Creates a new instance of ParetoDistribution
ParetoDistribution(double shape, double scale, double shift) Creates a new instance of ParetoDistribution
ParetoDistribution(ParetoDistribution other) Copy constructor

Method Summary

Modifier and Type	Method and Description
ParetoDistribution	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.
ParetoDistribution.CDF	getCDF() Gets the CDF of a scalar distribution.
java.lang.Double	getMaxSupport() Gets the minimum support (domain or input) of the distribution.
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.
ParetoDistribution.PDF	getProbabilityFunction() Gets the distribution function associated with this Distribution, either the PDF or PMF.
double	getScale() Getter for scale.
double	getShape() Getter for shape
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	setScale(double scale) Setter for scale
void	setShape(double shape) Setter for shape
void	setShift(double shift) Setter for shift.
java.lang.String	toString()

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

getMean, 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

Field Detail

DEFAULT_SHAPE

public static final double DEFAULT_SHAPE

Default shape, 2.0.

See Also:

Constant Field Values

DEFALUT_SCALE

public static final double DEFALUT_SCALE

Default scale, 1.0.

See Also:

Constant Field Values

DEFAULT_SHIFT

public static final double DEFAULT_SHIFT

Default shift, 0.0.

See Also:

Constant Field Values

shape

protected double shape

Scale parameter, must be greater than zero.

scale

protected double scale

Scale parameter, must be greater than zero.

shift

protected double shift

Amount to shift the distribution to the left.

Constructor Detail

ParetoDistribution

public ParetoDistribution()

Creates a new instance of ParetoDistribution

ParetoDistribution

public ParetoDistribution(double shape,
                          double scale,
                          double shift)

Creates a new instance of ParetoDistribution

Parameters:

shape - Scale parameter, must be greater than zero.

scale - Scale parameter, must be greater than zero.

shift - Amount to shift the distribution to the left.

ParetoDistribution

public ParetoDistribution(ParetoDistribution other)

Copy constructor

Parameters:

other - ParetoDistribution to copy

Method Detail

clone

public ParetoDistribution 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.

getShape

public double getShape()

Getter for shape

Returns:

Shape parameter, must be greater than zero.

setShape

public void setShape(double shape)

Setter for shape

Parameters:

shape - Shape parameter, must be greater than zero.

getScale

public double getScale()

Getter for scale.

Returns:

Scale parameter, must be greater than zero.

setScale

public void setScale(double scale)

Setter for scale

Parameters:

scale - Scale parameter, must be greater than zero.

getMeanAsDouble

public double getMeanAsDouble()

Description copied from interface: UnivariateDistribution

Gets the mean of the distribution as a 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.

Returns:

Variance of the distribution.

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.

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.

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.

Parameters:

parameters - The parameters to incorporate.

getProbabilityFunction

public ParetoDistribution.PDF getProbabilityFunction()

Description copied from interface: ComputableDistribution

Gets the distribution function associated with this Distribution, either the PDF or PMF.

Returns:

Distribution function associated with this Distribution.

getCDF

public ParetoDistribution.CDF getCDF()

Description copied from interface: UnivariateDistribution

Gets the CDF of a scalar distribution.

Returns:

CDF of the scalar distribution.

getMinSupport

public java.lang.Double getMinSupport()

Description copied from interface: UnivariateDistribution

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

Returns:

Minimum support.

getMaxSupport

public java.lang.Double getMaxSupport()

Description copied from interface: UnivariateDistribution

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

Returns:

Minimum support.

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

setShift

public void setShift(double shift)

Setter for shift.

Parameters:

shift - Amount to shift the distribution to the left.