Package org.hipparchus.distribution.continuous

Class EnumeratedRealDistribution

java.lang.Object

org.hipparchus.distribution.continuous.AbstractRealDistribution

org.hipparchus.distribution.continuous.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.

See Also:

Serialized Form

Field Summary

Fields inherited from class org.hipparchus.distribution.continuous.AbstractRealDistribution

DEFAULT_SOLVER_ABSOLUTE_ACCURACY

Constructor Summary

Constructors

Constructor	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.

Method Summary

Modifier and Type	Method	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.
List<Pair<Double,Double>>	getPmf()	Return the probability mass function as a list of (value, probability) pairs.
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. whether all values between the lower and upper bound of the support are included in the support.
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 org.hipparchus.distribution.continuous.AbstractRealDistribution

getSolverAbsoluteAccuracy, logDensity, probability

Methods inherited from class java.lang.Object

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

Constructor Detail

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

EnumeratedRealDistribution

public EnumeratedRealDistribution(double[] singletons,
                                  double[] probabilities)
                           throws MathIllegalArgumentException

Create a discrete real-valued distribution using the given probability mass function enumeration.

Parameters:

singletons - array of random variable values.

probabilities - array of probabilities.

Throws:

MathIllegalArgumentException - if singletons.length != probabilities.length

MathIllegalArgumentException - if any of the probabilities are negative.

MathIllegalArgumentException - if any of the probabilities are NaN.

MathIllegalArgumentException - if any of the probabilities are infinite.

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.

Note that if x1 and x2 satisfy x1.equals(x2), or both are null, then probability(x1) = probability(x2).

Parameters:

x - the point at which the PMF is evaluated

Returns:

the value of the probability mass function at 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.

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 MathIllegalArgumentException

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

• RealDistribution.getSupportLowerBound() for p = 0,
• RealDistribution.getSupportUpperBound() for p = 1.

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:

MathIllegalArgumentException - 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.

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

getPmf

public List<Pair<Double,Double>> getPmf()

Return the probability mass function as a list of (value, probability) pairs.

Returns:

the probability mass function.