gov.sandia.cognition.statistics

Class ProbabilityMassFunctionUtil

java.lang.Object

gov.sandia.cognition.statistics.ProbabilityMassFunctionUtil

public class ProbabilityMassFunctionUtil
extends java.lang.Object

Utility methods for helping computations in PMFs.

Since:

3.0

Author:

Kevin R. Dixon

Constructor Summary

Constructors

Constructor and Description
ProbabilityMassFunctionUtil()

Method Summary

Modifier and Type	Method and Description
static double	computeCumulativeValue(int input, ClosedFormDiscreteUnivariateDistribution<? super java.lang.Integer> distribution) Computes the CDF value for the given PMF for the input.
static <DataType> double	getEntropy(ProbabilityMassFunction<DataType> pmf) Computes the information-theoretic entropy of the PMF in bits.
static <DataType extends java.lang.Number> InputOutputPair<DataType,java.lang.Double>	inverse(CumulativeDistributionFunction<DataType> cdf, double p) Inverts the discrete CDF, that is p=Pr{x<=X}.
static <DataType> DataType	sample(double[] cumulativeWeights, java.util.List<? extends DataType> domain, java.util.Random random) Samples an element from the domain proportionately to the cumulative weights in the given weight array using a fast binary search algorithm.
static <DataType> java.util.ArrayList<DataType>	sample(ProbabilityMassFunction<DataType> pmf, java.util.Random random, int numSamples) Samples from the ProbabilityMassFunction.
static <DataType> void	sampleInto(ProbabilityMassFunction<DataType> pmf, java.util.Random random, int numSamples, java.util.Collection<? super DataType> output) Samples from the ProbabilityMassFunction.
static <DataType> java.util.ArrayList<DataType>	sampleMultiple(double[] cumulativeWeights, java.util.List<? extends DataType> domain, java.util.Random random, int numSamples) Samples multiple elements from the domain proportionately to the cumulative weights in the given weight array using a fast binary search algorithm
static <DataType> java.util.ArrayList<DataType>	sampleMultiple(ProbabilityMassFunction<DataType> pmf, java.util.Random random, int numSamples) Samples from the ProbabilityMassFunction.
static <DataType> void	sampleMultipleInto(double[] cumulativeWeights, java.util.List<? extends DataType> domain, java.util.Random random, int numSamples, java.util.Collection<? super DataType> output) Samples multiple elements from the domain proportionately to the cumulative weights in the given weight array using a fast binary search algorithm
static <DataType> void	sampleMultipleInto(ProbabilityMassFunction<DataType> pmf, java.util.Random random, int numSamples, java.util.Collection<? super DataType> output) Samples from the ProbabilityMassFunction.
static <DataType> DataType	sampleSingle(double[] weights, java.util.Collection<? extends DataType> domain, java.util.Random random) Samples a single element from the domain proportionately to the given weights
static <DataType> DataType	sampleSingle(ProbabilityMassFunction<DataType> pmf, java.util.Random random) Draws a single sample from the given PMF

Methods inherited from class java.lang.Object

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

Constructor Detail

ProbabilityMassFunctionUtil

public ProbabilityMassFunctionUtil()

Method Detail

getEntropy

@PublicationReference(author="Wikipedia",
                      title="Entropy (information theory)",
                      type=WebPage,
                      year=2009,
                      url="http://en.wikipedia.org/wiki/Entropy_(Information_theory)")
public static <DataType> double getEntropy(ProbabilityMassFunction<DataType> pmf)

Computes the information-theoretic entropy of the PMF in bits.

Type Parameters:

DataType - Type of data on the domain of the PMF.

Parameters:

pmf - PMF to compute the entropy.

Returns:

Entropy in bits of the given PMF.

sample

public static <DataType> java.util.ArrayList<DataType> sample(ProbabilityMassFunction<DataType> pmf,
                                                              java.util.Random random,
                                                              int numSamples)

Samples from the ProbabilityMassFunction. The return value will be sampled according to the given PMF.

Type Parameters:

DataType - Type of data to use

Parameters:

pmf - PMF from which to sample

random - Random to sample from

numSamples - Number of samples to draw from the given PMF.

Returns:

Samples drawn according to the given PMF.

sampleInto

public static <DataType> void sampleInto(ProbabilityMassFunction<DataType> pmf,
                                         java.util.Random random,
                                         int numSamples,
                                         java.util.Collection<? super DataType> output)

Samples from the ProbabilityMassFunction. The return value will be sampled according to the given PMF.

Type Parameters:

DataType - Type of data to use

Parameters:

pmf - PMF from which to sample

random - Random to sample from

numSamples - Number of samples to draw from the given PMF.

output - Collection to add samples drawn according to the given PMF.

sampleSingle

public static <DataType> DataType sampleSingle(ProbabilityMassFunction<DataType> pmf,
                                               java.util.Random random)

Draws a single sample from the given PMF

Type Parameters:

DataType - Type of observations generated by the PMF

Parameters:

pmf - PMF from which to draw.

random - Random number generator

Returns:

Single sample from the PMF

sampleMultiple

public static <DataType> java.util.ArrayList<DataType> sampleMultiple(ProbabilityMassFunction<DataType> pmf,
                                                                      java.util.Random random,
                                                                      int numSamples)

Samples from the ProbabilityMassFunction. The return value will be sampled according to the given PMF.

Type Parameters:

DataType - Type of data to use

Parameters:

pmf - PMF from which to sample

random - Random to sample from

numSamples - Number of samples to draw from the given PMF.

Returns:

Samples drawn according to the given PMF.

sampleMultipleInto

public static <DataType> void sampleMultipleInto(ProbabilityMassFunction<DataType> pmf,
                                                 java.util.Random random,
                                                 int numSamples,
                                                 java.util.Collection<? super DataType> output)

Samples from the ProbabilityMassFunction. The return value will be sampled according to the given PMF.

Type Parameters:

DataType - Type of data to use

Parameters:

pmf - PMF from which to sample

random - Random to sample from

numSamples - Number of samples to draw from the given PMF.

output - Collection to add samples drawn according to the given PMF.

sampleMultiple

public static <DataType> java.util.ArrayList<DataType> sampleMultiple(double[] cumulativeWeights,
                                                                      java.util.List<? extends DataType> domain,
                                                                      java.util.Random random,
                                                                      int numSamples)

Samples multiple elements from the domain proportionately to the cumulative weights in the given weight array using a fast binary search algorithm

Type Parameters:

DataType - Type of data to be sampled

Parameters:

cumulativeWeights - Cumulative weights to sample from

domain - Domain from which to sample

random - Random number generator

numSamples - Number of samples to draw from the distribution

Returns:

Samples draw proportionately from the cumulative weights

sampleMultipleInto

public static <DataType> void sampleMultipleInto(double[] cumulativeWeights,
                                                 java.util.List<? extends DataType> domain,
                                                 java.util.Random random,
                                                 int numSamples,
                                                 java.util.Collection<? super DataType> output)

Samples multiple elements from the domain proportionately to the cumulative weights in the given weight array using a fast binary search algorithm

Type Parameters:

DataType - Type of data to be sampled

Parameters:

cumulativeWeights - Cumulative weights to sample from

domain - Domain from which to sample

random - Random number generator

numSamples - Number of samples to draw from the distribution

output - The collection to put the samples in.

sample

public static <DataType> DataType sample(double[] cumulativeWeights,
                                         java.util.List<? extends DataType> domain,
                                         java.util.Random random)

Samples an element from the domain proportionately to the cumulative weights in the given weight array using a fast binary search algorithm.

Type Parameters:

DataType - Type of data to be sampled

Parameters:

cumulativeWeights - Cumulative weights to sample from

domain - Domain from which to sample

random - Random number generator

Returns:

A sample from the domain according to the weights.

sampleSingle

public static <DataType> DataType sampleSingle(double[] weights,
                                               java.util.Collection<? extends DataType> domain,
                                               java.util.Random random)

Samples a single element from the domain proportionately to the given weights

Type Parameters:

DataType - Type of data to be sampled

Parameters:

weights - Weights from which we will sample proportionately

domain - Domain from which to return the result

random - Random number generator

Returns:

A single sample from the domain proportionately from the weights

inverse

public static <DataType extends java.lang.Number> InputOutputPair<DataType,java.lang.Double> inverse(CumulativeDistributionFunction<DataType> cdf,
                                                                                                     double p)

Inverts the discrete CDF, that is p=Pr{x<=X}.

Type Parameters:

DataType - Type of number from the distribution

Parameters:

cdf - CDF of a discrete distribution.

p - Probability to invert, must be [0,1].

Returns:

Value of x such that p >= CDF(x) and p <= CDF(x_next).

computeCumulativeValue

public static double computeCumulativeValue(int input,
                                            ClosedFormDiscreteUnivariateDistribution<? super java.lang.Integer> distribution)

Computes the CDF value for the given PMF for the input. That is, the value of P=CDF(input)=sum(PMF(x<=input)).

Parameters:

input - Input to compute the CDF of.

distribution - Distribution to consider.

Returns:

CDF value of the distirbution for the given input