Top Description Fields Constructors Methods
org.apache.commons.math3.distribution

public Class BinomialDistribution

extends AbstractIntegerDistribution
Class Inheritance
Imports
org.apache.commons.math3.exception.NotPositiveException, .OutOfRangeException, org.apache.commons.math3.exception.util.LocalizedFormats, org.apache.commons.math3.random.RandomGenerator, .Well19937c, org.apache.commons.math3.special.Beta, org.apache.commons.math3.util.FastMath
Implementation of the binomial distribution.
See Also
Binomial distribution (Wikipedia), Binomial Distribution (MathWorld)

Field Summary

Modifier and TypeField and Description
private final int
numberOfTrials

The number of trials.

private final double
probabilityOfSuccess

The probability of success.

private static final long
serialVersionUID

Hides org.apache.commons.math3.distribution.AbstractIntegerDistribution.serialVersionUID.

Serializable version identifier.
Inherited from org.apache.commons.math3.distribution.AbstractIntegerDistribution:
randomrandomData

Constructor Summary

AccessConstructor and Description
public
BinomialDistribution(int
Number of trials.
trials, double
Probability of success.
p)

Create a binomial distribution with the given number of trials and probability of success.

public
BinomialDistribution(RandomGenerator
Random number generator.
rng, int
Number of trials.
trials, double
Probability of success.
p)

Creates a binomial distribution.

Method Summary

Modifier and TypeMethod and Description
public double
cumulativeProbability(int
the point at which the CDF is evaluated
x)

Implements org.apache.commons.math3.distribution.IntegerDistribution.cumulativeProbability.

For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).

public int

Returns:

the number of trials.
getNumberOfTrials()

Access the number of trials for this distribution.

public double
getNumericalMean()

Implements org.apache.commons.math3.distribution.IntegerDistribution.getNumericalMean.

Use this method to get the numerical value of the mean of this distribution.

public double
getNumericalVariance()

Implements org.apache.commons.math3.distribution.IntegerDistribution.getNumericalVariance.

Use this method to get the numerical value of the variance of this distribution.

public double

Returns:

the probability of success.
getProbabilityOfSuccess()

Access the probability of success for this distribution.

public int

Returns:

lower bound of the support (0 or the number of trials)
getSupportLowerBound()

Implements org.apache.commons.math3.distribution.IntegerDistribution.getSupportLowerBound.

Access the lower bound of the support.

public int

Returns:

upper bound of the support (number of trials or 0)
getSupportUpperBound()

Implements org.apache.commons.math3.distribution.IntegerDistribution.getSupportUpperBound.

Access the upper bound of the support.

public boolean

Returns:

true
isSupportConnected()

Implements org.apache.commons.math3.distribution.IntegerDistribution.isSupportConnected.

Use this method to get information about whether the support is connected, i.e. whether all integers between the lower and upper bound of the support are included in the support.

public double
logProbability(int
the point at which the PMF is evaluated
x)

Overrides org.apache.commons.math3.distribution.AbstractIntegerDistribution.logProbability.

For a random variable X whose values are distributed according to this distribution, this method returns log(P(X = x)), where log is the natural logarithm.

public double
probability(int
the point at which the PMF is evaluated
x)

Implements org.apache.commons.math3.distribution.IntegerDistribution.probability.

For a random variable X whose values are distributed according to this distribution, this method returns P(X = x).

Inherited from org.apache.commons.math3.distribution.AbstractIntegerDistribution:
cumulativeProbabilityinverseCumulativeProbabilityreseedRandomGeneratorsamplesamplesolveInverseCumulativeProbability

Field Detail

numberOfTrialsback to summary
private final int numberOfTrials

The number of trials.

probabilityOfSuccessback to summary
private final double probabilityOfSuccess

The probability of success.

serialVersionUIDback to summary
private static final long serialVersionUID

Hides org.apache.commons.math3.distribution.AbstractIntegerDistribution.serialVersionUID.

Serializable version identifier.

Constructor Detail

BinomialDistributionback to summary
public BinomialDistribution(int trials, double p)

Create a binomial distribution with the given number of trials and probability of success.

Note

this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see sample() and 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
trials:int

Number of trials.

p:double

Probability of success.

Exceptions
NotPositiveException:
if trials < 0.
OutOfRangeException:
if p < 0 or p > 1.
BinomialDistributionback to summary
public BinomialDistribution(RandomGenerator rng, int trials, double p)

Creates a binomial distribution.

Parameters
rng:RandomGenerator

Random number generator.

trials:int

Number of trials.

p:double

Probability of success.

Exceptions
NotPositiveException:
if trials < 0.
OutOfRangeException:
if p < 0 or p > 1.
Since
3.1

Method Detail

cumulativeProbabilityback to summary
public double cumulativeProbability(int x)

Implements org.apache.commons.math3.distribution.IntegerDistribution.cumulativeProbability.

Doc from org.apache.commons.math3.distribution.IntegerDistribution.cumulativeProbability.

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:int

the point at which the CDF is evaluated

Returns:double

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

getNumberOfTrialsback to summary
public int getNumberOfTrials()

Access the number of trials for this distribution.

Returns:int

the number of trials.

getNumericalMeanback to summary
public double getNumericalMean()

Implements org.apache.commons.math3.distribution.IntegerDistribution.getNumericalMean.

Doc from org.apache.commons.math3.distribution.IntegerDistribution.getNumericalMean.

Use this method to get the numerical value of the mean of this distribution. For n trials and probability parameter p, the mean is n * p.

Returns:double

the mean or Double.NaN if it is not defined

getNumericalVarianceback to summary
public double getNumericalVariance()

Implements org.apache.commons.math3.distribution.IntegerDistribution.getNumericalVariance.

Doc from org.apache.commons.math3.distribution.IntegerDistribution.getNumericalVariance.

Use this method to get the numerical value of the variance of this distribution. For n trials and probability parameter p, the variance is n * p * (1 - p).

Returns:double

the variance (possibly Double.POSITIVE_INFINITY or Double.NaN if it is not defined)

getProbabilityOfSuccessback to summary
public double getProbabilityOfSuccess()

Access the probability of success for this distribution.

Returns:double

the probability of success.

getSupportLowerBoundback to summary
public int getSupportLowerBound()

Implements org.apache.commons.math3.distribution.IntegerDistribution.getSupportLowerBound.

Doc from org.apache.commons.math3.distribution.IntegerDistribution.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 Z | P(X <= x) > 0}.

The lower bound of the support is always 0 except for the probability parameter p = 1.
Returns:int

lower bound of the support (0 or the number of trials)

getSupportUpperBoundback to summary
public int getSupportUpperBound()

Implements org.apache.commons.math3.distribution.IntegerDistribution.getSupportUpperBound.

Doc from org.apache.commons.math3.distribution.IntegerDistribution.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}.

The upper bound of the support is the number of trials except for the probability parameter p = 0.
Returns:int

upper bound of the support (number of trials or 0)

isSupportConnectedback to summary
public boolean isSupportConnected()

Implements org.apache.commons.math3.distribution.IntegerDistribution.isSupportConnected.

Doc from org.apache.commons.math3.distribution.IntegerDistribution.isSupportConnected.

Use this method to get information about whether the support is connected, i.e. whether all integers between the lower and upper bound of the support are included in the support. The support of this distribution is connected.

Returns:boolean

true

logProbabilityback to summary
public double logProbability(int x)

Overrides org.apache.commons.math3.distribution.AbstractIntegerDistribution.logProbability.

Doc from org.apache.commons.math3.distribution.AbstractIntegerDistribution.logProbability.

For a random variable X whose values are distributed according to this distribution, this method returns log(P(X = x)), where log is the natural logarithm. In other words, this method represents the logarithm of the probability mass function (PMF) for the distribution. Note that due to the floating point precision and under/overflow issues, this method will for some distributions be more precise and faster than computing the logarithm of probability(int).

The default implementation simply computes the logarithm of probability(x).

Parameters
x:int

the point at which the PMF is evaluated

Returns:double

the logarithm of the value of the probability mass function at x

Annotations
@Override
probabilityback to summary
public double probability(int x)

Implements org.apache.commons.math3.distribution.IntegerDistribution.probability.

Doc from org.apache.commons.math3.distribution.IntegerDistribution.probability.

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:int

the point at which the PMF is evaluated

Returns:double

the value of the probability mass function at x