Package org.apache.commons.math4.distribution

Class EnumeratedRealDistribution

java.lang.Object

org.apache.commons.math4.distribution.EnumeratedRealDistribution

All Implemented Interfaces:

java.io.Serializable, ContinuousDistribution

public class EnumeratedRealDistribution
extends java.lang.Object
implements ContinuousDistribution, java.io.Serializable

Implementation of a real-valued EnumeratedDistribution.

Values with zero-probability are allowed but they do not extend the support.
Duplicate values are allowed. Probabilities of duplicate values are combined when computing cumulative probabilities and statistics.

Since:

3.2

See Also:

Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution

ContinuousDistribution.Sampler

Field Summary

Fields

Modifier and Type	Field	Description
protected EnumeratedDistribution<java.lang.Double>	innerDistribution	EnumeratedDistribution (using the Double wrapper) used to generate the pmf.

Constructor Summary

Constructors

Constructor	Description
EnumeratedRealDistribution(double[] data)	Creates a discrete real-valued distribution from the input data.
EnumeratedRealDistribution(double[] singletons, double[] probabilities)	Create a discrete real-valued distribution using the given random number generator and probability mass function enumeration.

Method Summary

Modifier and Type	Method	Description
ContinuousDistribution.Sampler	createSampler(UniformRandomProvider rng)	Creates a sampler.
double	cumulativeProbability(double x)	For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
double	density(double x)	For a random variable X whose values are distributed according to this distribution, this method returns P(X = x).
double	getMean()	Gets the mean of this distribution.
double	getSupportLowerBound()	Gets the lower bound of the support.
double	getSupportUpperBound()	Gets the upper bound of the support.
double	getVariance()	Gets the variance of this distribution.
double	inverseCumulativeProbability(double p)	Computes the quantile function of this distribution.
boolean	isSupportConnected()	Indicates whether the support is connected, i.e.
double	probability(double x)	For a random variable X whose values are distributed according to this distribution, this method returns P(X = x).

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution

logDensity, probability

Field Detail

innerDistribution

protected final EnumeratedDistribution<java.lang.Double> innerDistribution

EnumeratedDistribution (using the Double wrapper) used to generate the pmf.

Constructor Detail

EnumeratedRealDistribution

public EnumeratedRealDistribution(double[] singletons,
                                  double[] probabilities)
                           throws DimensionMismatchException,
                                  NotPositiveException,
                                  MathArithmeticException,
                                  NotFiniteNumberException,
                                  NotANumberException

Create a discrete real-valued distribution using the given random number generator and probability mass function enumeration.

Parameters:

singletons - array of random variable values.

probabilities - array of probabilities.

Throws:

DimensionMismatchException - if singletons.length != probabilities.length

NotPositiveException - if any of the probabilities are negative.

NotFiniteNumberException - if any of the probabilities are infinite.

NotANumberException - if any of the probabilities are NaN.

MathArithmeticException - all of the probabilities are 0.

EnumeratedRealDistribution

public EnumeratedRealDistribution(double[] data)

Creates a discrete real-valued distribution from the input data. Values are assigned mass based on their frequency.

Parameters:

data - input dataset

Method Detail

probability

public double probability(double x)

For a random variable X whose values are distributed according to this distribution, this method returns P(X = x). In other words, this method represents the probability mass function (PMF) for the distribution.

Specified by:

probability in interface ContinuousDistribution

Parameters:

x - Point at which the PMF is evaluated.

Returns:

the value of the probability mass function at point x.

density

public double density(double x)

For a random variable X whose values are distributed according to this distribution, this method returns P(X = x). In other words, this method represents the probability mass function (PMF) for the distribution.

Specified by:

density in interface ContinuousDistribution

Parameters:

x - the point at which the PMF is evaluated

Returns:

the value of the probability mass function at point x

cumulativeProbability

public double cumulativeProbability(double x)

For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x). In other words, this method represents the (cumulative) distribution function (CDF) for this distribution.

Specified by:

cumulativeProbability in interface ContinuousDistribution

Parameters:

x - Point at which the CDF is evaluated.

Returns:

the probability that a random variable with this distribution takes a value less than or equal to x.

inverseCumulativeProbability

public double inverseCumulativeProbability(double p)
                                    throws OutOfRangeException

Computes the quantile function of this distribution. For a random variable X distributed according to this distribution, the returned value is

• inf{x in R | P(X<=x) >= p} for 0 < p <= 1,
• inf{x in R | P(X<=x) > 0} for p = 0.

Specified by:

inverseCumulativeProbability in interface ContinuousDistribution

Parameters:

p - Cumulative probability.

Returns:

the smallest p-quantile of this distribution (largest 0-quantile for p = 0).

Throws:

OutOfRangeException

getMean

public double getMean()

Gets the mean of this distribution.

Specified by:

getMean in interface ContinuousDistribution

Returns:

sum(singletons[i] * probabilities[i])

getVariance

public double getVariance()

Gets the variance of this distribution.

Specified by:

getVariance in interface ContinuousDistribution

Returns:

sum((singletons[i] - mean) ^ 2 * probabilities[i])

getSupportLowerBound

public double getSupportLowerBound()

Gets the lower bound of the support. It must return the same value as inverseCumulativeProbability(0), i.e. inf {x in R | P(X <= x) > 0}. Returns the lowest value with non-zero probability.

Specified by:

getSupportLowerBound in interface ContinuousDistribution

Returns:

the lowest value with non-zero probability.

getSupportUpperBound

public double getSupportUpperBound()

Gets the upper bound of the support. It must return the same value as inverseCumulativeProbability(1), i.e. inf {x in R | P(X <= x) = 1}. Returns the highest value with non-zero probability.

Specified by:

getSupportUpperBound in interface ContinuousDistribution

Returns:

the highest value with non-zero probability.

isSupportConnected

public boolean isSupportConnected()

Indicates whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support. The support of this distribution is connected.

Specified by:

isSupportConnected in interface ContinuousDistribution

Returns:

true

createSampler

public ContinuousDistribution.Sampler createSampler(UniformRandomProvider rng)

Creates a sampler.

Specified by:

createSampler in interface ContinuousDistribution

Parameters:

rng - Generator of uniformly distributed numbers.

Returns:

a sampler that produces random numbers according this distribution.