Class HypergeometricDistribution
java.lang.Object
org.apache.commons.math3.distribution.AbstractIntegerDistribution
org.apache.commons.math3.distribution.HypergeometricDistribution
- All Implemented Interfaces:
Serializable
,IntegerDistribution
Implementation of the hypergeometric distribution.
- See Also:
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Field Summary
FieldsModifier and TypeFieldDescriptionprivate final int
The number of successes in the population.private double
Cached numerical varianceprivate boolean
Whether or not the numerical variance has been calculatedprivate final int
The population size.private final int
The sample size.private static final long
Serializable version identifier.Fields inherited from class org.apache.commons.math3.distribution.AbstractIntegerDistribution
random, randomData
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Constructor Summary
ConstructorsConstructorDescriptionHypergeometricDistribution
(int populationSize, int numberOfSuccesses, int sampleSize) Construct a new hypergeometric distribution with the specified population size, number of successes in the population, and sample size.HypergeometricDistribution
(RandomGenerator rng, int populationSize, int numberOfSuccesses, int sampleSize) Creates a new hypergeometric distribution. -
Method Summary
Modifier and TypeMethodDescriptionprotected double
Used bygetNumericalVariance()
.double
cumulativeProbability
(int x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X <= x)
.private int[]
getDomain
(int n, int m, int k) Return the domain for the given hypergeometric distribution parameters.private int
getLowerDomain
(int n, int m, int k) Return the lowest domain value for the given hypergeometric distribution parameters.int
Access the number of successes.double
Use this method to get the numerical value of the mean of this distribution.double
Use this method to get the numerical value of the variance of this distribution.int
Access the population size.int
Access the sample size.int
Access the lower bound of the support.int
Access the upper bound of the support.private int
getUpperDomain
(int m, int k) Return the highest domain value for the given hypergeometric distribution parameters.private double
innerCumulativeProbability
(int x0, int x1, int dx) For this distribution,X
, this method returnsP(x0 <= X <= x1)
.boolean
Use this method to get information about whether the support is connected, i.e.double
logProbability
(int x) For a random variableX
whose values are distributed according to this distribution, this method returnslog(P(X = x))
, wherelog
is the natural logarithm.double
probability
(int x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X = x)
.double
upperCumulativeProbability
(int x) For this distribution,X
, this method returnsP(X >= x)
.Methods inherited from class org.apache.commons.math3.distribution.AbstractIntegerDistribution
cumulativeProbability, inverseCumulativeProbability, reseedRandomGenerator, sample, sample, solveInverseCumulativeProbability
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Field Details
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serialVersionUID
private static final long serialVersionUIDSerializable version identifier.- See Also:
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numberOfSuccesses
private final int numberOfSuccessesThe number of successes in the population. -
populationSize
private final int populationSizeThe population size. -
sampleSize
private final int sampleSizeThe sample size. -
numericalVariance
private double numericalVarianceCached numerical variance -
numericalVarianceIsCalculated
private boolean numericalVarianceIsCalculatedWhether or not the numerical variance has been calculated
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Constructor Details
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HypergeometricDistribution
public HypergeometricDistribution(int populationSize, int numberOfSuccesses, int sampleSize) throws NotPositiveException, NotStrictlyPositiveException, NumberIsTooLargeException Construct a new hypergeometric distribution with the specified population size, number of successes in the population, and sample size.Note: this constructor will implicitly create an instance of
Well19937c
as random generator to be used for sampling only (seeAbstractIntegerDistribution.sample()
andAbstractIntegerDistribution.sample(int)
). In case no sampling is needed for the created distribution, it is advised to passnull
as random generator via the appropriate constructors to avoid the additional initialisation overhead.- Parameters:
populationSize
- Population size.numberOfSuccesses
- Number of successes in the population.sampleSize
- Sample size.- Throws:
NotPositiveException
- ifnumberOfSuccesses < 0
.NotStrictlyPositiveException
- ifpopulationSize <= 0
.NumberIsTooLargeException
- ifnumberOfSuccesses > populationSize
, orsampleSize > populationSize
.
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HypergeometricDistribution
public HypergeometricDistribution(RandomGenerator rng, int populationSize, int numberOfSuccesses, int sampleSize) throws NotPositiveException, NotStrictlyPositiveException, NumberIsTooLargeException Creates a new hypergeometric distribution.- Parameters:
rng
- Random number generator.populationSize
- Population size.numberOfSuccesses
- Number of successes in the population.sampleSize
- Sample size.- Throws:
NotPositiveException
- ifnumberOfSuccesses < 0
.NotStrictlyPositiveException
- ifpopulationSize <= 0
.NumberIsTooLargeException
- ifnumberOfSuccesses > populationSize
, orsampleSize > populationSize
.- Since:
- 3.1
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Method Details
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cumulativeProbability
public double cumulativeProbability(int x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(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
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getDomain
private int[] getDomain(int n, int m, int k) Return the domain for the given hypergeometric distribution parameters.- Parameters:
n
- Population size.m
- Number of successes in the population.k
- Sample size.- Returns:
- a two element array containing the lower and upper bounds of the hypergeometric distribution.
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getLowerDomain
private int getLowerDomain(int n, int m, int k) Return the lowest domain value for the given hypergeometric distribution parameters.- Parameters:
n
- Population size.m
- Number of successes in the population.k
- Sample size.- Returns:
- the lowest domain value of the hypergeometric distribution.
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getNumberOfSuccesses
public int getNumberOfSuccesses()Access the number of successes.- Returns:
- the number of successes.
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getPopulationSize
public int getPopulationSize()Access the population size.- Returns:
- the population size.
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getSampleSize
public int getSampleSize()Access the sample size.- Returns:
- the sample size.
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getUpperDomain
private int getUpperDomain(int m, int k) Return the highest domain value for the given hypergeometric distribution parameters.- Parameters:
m
- Number of successes in the population.k
- Sample size.- Returns:
- the highest domain value of the hypergeometric distribution.
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probability
public double probability(int x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(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
x
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logProbability
public double logProbability(int x) For a random variableX
whose values are distributed according to this distribution, this method returnslog(P(X = x))
, wherelog
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 ofIntegerDistribution.probability(int)
.The default implementation simply computes the logarithm of
probability(x)
.- Overrides:
logProbability
in classAbstractIntegerDistribution
- Parameters:
x
- the point at which the PMF is evaluated- Returns:
- the logarithm of the value of the probability mass function at
x
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upperCumulativeProbability
public double upperCumulativeProbability(int x) For this distribution,X
, this method returnsP(X >= x)
.- Parameters:
x
- Value at which the CDF is evaluated.- Returns:
- the upper tail CDF for this distribution.
- Since:
- 1.1
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innerCumulativeProbability
private double innerCumulativeProbability(int x0, int x1, int dx) For this distribution,X
, this method returnsP(x0 <= X <= x1)
. This probability is computed by summing the point probabilities for the valuesx0, x0 + 1, x0 + 2, ..., x1
, in the order directed bydx
.- Parameters:
x0
- Inclusive lower bound.x1
- Inclusive upper bound.dx
- Direction of summation (1 indicates summing from x0 to x1, and 0 indicates summing from x1 to x0).- Returns:
P(x0 <= X <= x1)
.
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getNumericalMean
public double getNumericalMean()Use this method to get the numerical value of the mean of this distribution. For population sizeN
, number of successesm
, and sample sizen
, the mean isn * m / N
.- Returns:
- the mean or
Double.NaN
if it is not defined
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getNumericalVariance
public double getNumericalVariance()Use this method to get the numerical value of the variance of this distribution. For population sizeN
, number of successesm
, and sample sizen
, the variance is[n * m * (N - n) * (N - m)] / [N^2 * (N - 1)]
.- Returns:
- the variance (possibly
Double.POSITIVE_INFINITY
orDouble.NaN
if it is not defined)
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calculateNumericalVariance
protected double calculateNumericalVariance()Used bygetNumericalVariance()
.- Returns:
- the variance of this distribution
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getSupportLowerBound
public int getSupportLowerBound()Access the lower bound of the support. This method must return the same value asinverseCumulativeProbability(0)
. In other words, this method must return
For population sizeinf {x in Z | P(X invalid input: '<'= x) > 0}
.N
, number of successesm
, and sample sizen
, the lower bound of the support ismax(0, n + m - N)
.- Returns:
- lower bound of the support
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getSupportUpperBound
public int getSupportUpperBound()Access the upper bound of the support. This method must return the same value asinverseCumulativeProbability(1)
. In other words, this method must return
For number of successesinf {x in R | P(X invalid input: '<'= x) = 1}
.m
and sample sizen
, the upper bound of the support ismin(m, n)
.- Returns:
- upper bound of the support
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isSupportConnected
public boolean 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:
true
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