org.apache.commons.math3.distribution

## Class EnumeratedRealDistribution

• All Implemented Interfaces:
Serializable, RealDistribution

public class EnumeratedRealDistribution
extends AbstractRealDistribution

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
Serialized Form
• ### Field Summary

Fields
Modifier and Type Field and Description
protected EnumeratedDistribution<Double> innerDistribution
EnumeratedDistribution (using the Double wrapper) used to generate the pmf.
• ### Fields inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY
• ### Constructor Summary

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

Methods
Modifier and Type Method and Description
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 getNumericalMean()
Use this method to get the numerical value of the mean of this distribution.
double getNumericalVariance()
Use this method to get the numerical value of the variance of this distribution.
double getSupportLowerBound()
Access the lower bound of the support.
double getSupportUpperBound()
Access the upper bound of the support.
double inverseCumulativeProbability(double p)
Computes the quantile function of this distribution.
boolean isSupportConnected()
Use this method to get information about whether the support is connected, i.e.
boolean isSupportLowerBoundInclusive()
Whether or not the lower bound of support is in the domain of the density function.
boolean isSupportUpperBoundInclusive()
Whether or not the upper bound of support is in the domain of the density function.
double probability(double x)
For a random variable X whose values are distributed according to this distribution, this method returns P(X = x).
double sample()
Generate a random value sampled from this distribution.
• ### Methods inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

cumulativeProbability, getSolverAbsoluteAccuracy, logDensity, probability, reseedRandomGenerator, sample
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

• #### EnumeratedRealDistribution

public EnumeratedRealDistribution(double[] singletons,
double[] probabilities)
throws DimensionMismatchException,
NotPositiveException,
MathArithmeticException,
NotFiniteNumberException,
NotANumberException
Create a discrete real-valued distribution using the given probability mass function enumeration.

Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see sample() and AbstractRealDistribution.sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead.

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(RandomGenerator rng,
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:
rng - random number generator.
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(RandomGenerator rng,
double[] data)
Create a discrete real-valued distribution from the input data. Values are assigned mass based on their frequency.
Parameters:
rng - random number generator used for sampling
data - input dataset
Since:
3.6
• #### EnumeratedRealDistribution

public EnumeratedRealDistribution(double[] data)
Create a discrete real-valued distribution from the input data. Values are assigned mass based on their frequency. For example, [0,1,1,2] as input creates a distribution with values 0, 1 and 2 having probability masses 0.25, 0.5 and 0.25 respectively,
Parameters:
data - input dataset
Since:
3.6
• ### 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 RealDistribution
Overrides:
probability in class AbstractRealDistribution
Parameters:
x - the point at which the PMF is evaluated
Returns:
zero.
• #### 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.
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.
Parameters:
x - the 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.
The default implementation returns
Specified by:
inverseCumulativeProbability in interface RealDistribution
Overrides:
inverseCumulativeProbability in class AbstractRealDistribution
Parameters:
p - the cumulative probability
Returns:
the smallest p-quantile of this distribution (largest 0-quantile for p = 0)
Throws:
OutOfRangeException - if p < 0 or p > 1
• #### getNumericalMean

public double getNumericalMean()
Use this method to get the numerical value of the mean of this distribution.
Returns:
sum(singletons[i] * probabilities[i])
• #### getNumericalVariance

public double getNumericalVariance()
Use this method to get the numerical value of the variance of this distribution.
Returns:
sum((singletons[i] - mean) ^ 2 * probabilities[i])
• #### getSupportLowerBound

public double getSupportLowerBound()
Access the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0). In other words, this method must return

inf {x in R | P(X <= x) > 0}.

Returns the lowest value with non-zero probability.
Returns:
the lowest value with non-zero probability.
• #### getSupportUpperBound

public double getSupportUpperBound()
Access the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1). In other words, this method must return

inf {x in R | P(X <= x) = 1}.

Returns the highest value with non-zero probability.
Returns:
the highest value with non-zero probability.
• #### isSupportLowerBoundInclusive

public boolean isSupportLowerBoundInclusive()
Whether or not the lower bound of support is in the domain of the density function. Returns true iff getSupporLowerBound() is finite and density(getSupportLowerBound()) returns a non-NaN, non-infinite value. The support of this distribution includes the lower bound.
Returns:
true
• #### isSupportUpperBoundInclusive

public boolean isSupportUpperBoundInclusive()
Whether or not the upper bound of support is in the domain of the density function. Returns true iff getSupportUpperBound() is finite and density(getSupportUpperBound()) returns a non-NaN, non-infinite value. The support of this distribution includes the upper bound.
Returns:
true
• #### isSupportConnected

public boolean isSupportConnected()
Use this method to get information about 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.
Returns:
true
• #### sample

public double sample()
Generate a random value sampled from this distribution. The default implementation uses the inversion method.
Specified by:
sample in interface RealDistribution
Overrides:
sample in class AbstractRealDistribution
Returns:
a random value.