Class HypergeometricDistribution
- All Implemented Interfaces:
DiscreteDistribution
The probability mass function of \( X \) is:
\[ f(k; N, K, n) = \frac{\binom{K}{k} \binom{N - K}{n-k}}{\binom{N}{n}} \]
for \( N \in \{0, 1, 2, \dots\} \) the population size, \( K \in \{0, 1, \dots, N\} \) the number of success states, \( n \in \{0, 1, \dots, N\} \) the number of samples, \( k \in \{\max(0, n+K-N), \dots, \min(n, K)\} \) the number of successes, and
\[ \binom{a}{b} = \frac{a!}{b! \, (a-b)!} \]
is the binomial coefficient.
- See Also:
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Nested Class Summary
Nested classes/interfaces inherited from interface org.apache.commons.statistics.distribution.DiscreteDistribution
DiscreteDistribution.Sampler
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Field Summary
FieldsModifier and TypeFieldDescriptionprivate final int
The lower bound of the support (inclusive).private final int
The number of successes in the population.private final double
Binomial probability of success (sampleSize / populationSize).private final int
The population size.private final double
Binomial probability of failure ((populationSize - sampleSize) / populationSize).private final int
The sample size.private final int
The upper bound of the support (inclusive). -
Constructor Summary
ConstructorsModifierConstructorDescriptionprivate
HypergeometricDistribution
(int populationSize, int numberOfSuccesses, int sampleSize) -
Method Summary
Modifier and TypeMethodDescriptionprivate double
computeLogProbability
(int x) Compute the log probability.double
cumulativeProbability
(int x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X <= x)
.private static int
getLowerDomain
(int nn, int k, int n) Return the lowest domain value for the given hypergeometric distribution parameters.double
getMean()
Gets the mean of this distribution.int
Gets the number of successes parameter of this distribution.int
Gets the population size parameter of this distribution.int
Gets the sample size parameter of this distribution.int
Gets the lower bound of the support.int
Gets the upper bound of the support.private static int
getUpperDomain
(int k, int n) Return the highest domain value for the given hypergeometric distribution parameters.double
Gets the variance of this distribution.private double
innerCumulativeProbability
(int x0, int x1) For this distribution,X
, this method returnsP(x0 <= X <= x1)
.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.static HypergeometricDistribution
of
(int populationSize, int numberOfSuccesses, int sampleSize) Creates a hypergeometric distribution.double
probability
(int x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X = x)
.double
survivalProbability
(int x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X > x)
.Methods inherited from class org.apache.commons.statistics.distribution.AbstractDiscreteDistribution
createSampler, getMedian, inverseCumulativeProbability, inverseSurvivalProbability, probability
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Field Details
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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. -
lowerBound
private final int lowerBoundThe lower bound of the support (inclusive). -
upperBound
private final int upperBoundThe upper bound of the support (inclusive). -
p
private final double pBinomial probability of success (sampleSize / populationSize). -
q
private final double qBinomial probability of failure ((populationSize - sampleSize) / populationSize).
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Constructor Details
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HypergeometricDistribution
private HypergeometricDistribution(int populationSize, int numberOfSuccesses, int sampleSize) - Parameters:
populationSize
- Population size.numberOfSuccesses
- Number of successes in the population.sampleSize
- Sample size.
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Method Details
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of
public static HypergeometricDistribution of(int populationSize, int numberOfSuccesses, int sampleSize) Creates a hypergeometric distribution.- Parameters:
populationSize
- Population size.numberOfSuccesses
- Number of successes in the population.sampleSize
- Sample size.- Returns:
- the distribution
- Throws:
IllegalArgumentException
- ifnumberOfSuccesses < 0
, orpopulationSize <= 0
ornumberOfSuccesses > populationSize
, orsampleSize > populationSize
.
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getLowerDomain
private static int getLowerDomain(int nn, int k, int n) Return the lowest domain value for the given hypergeometric distribution parameters.- Parameters:
nn
- Population size.k
- Number of successes in the population.n
- Sample size.- Returns:
- the lowest domain value of the hypergeometric distribution.
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getUpperDomain
private static int getUpperDomain(int k, int n) Return the highest domain value for the given hypergeometric distribution parameters.- Parameters:
k
- Number of successes in the population.n
- Sample size.- Returns:
- the highest domain value of the hypergeometric distribution.
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getPopulationSize
public int getPopulationSize()Gets the population size parameter of this distribution.- Returns:
- the population size.
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getNumberOfSuccesses
public int getNumberOfSuccesses()Gets the number of successes parameter of this distribution.- Returns:
- the number of successes.
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getSampleSize
public int getSampleSize()Gets the sample size parameter of this distribution.- Returns:
- the sample size.
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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
- 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.- Parameters:
x
- Point at which the PMF is evaluated.- Returns:
- the logarithm of the value of the probability mass function at
x
.
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computeLogProbability
private double computeLogProbability(int x) Compute the log probability.- Parameters:
x
- Value.- Returns:
- log(P(X = x))
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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
- 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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survivalProbability
public double survivalProbability(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 complementary cumulative distribution function.By default, this is defined as
1 - cumulativeProbability(x)
, but the specific implementation may be more accurate.- Parameters:
x
- Point at which the survival function is evaluated.- Returns:
- the probability that a random variable with this
distribution takes a value greater than
x
.
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innerCumulativeProbability
private double innerCumulativeProbability(int x0, int x1) For this distribution,X
, this method returnsP(x0 <= X <= x1)
. This probability is computed by summing the point probabilities for the valuesx0, x0 + dx, x0 + 2 * dx, ..., x1
; the directiondx
is determined using a comparison of the input bounds. This should be called by usingx0
as the domain limit andx1
as the internal value. This will result in an initial sum of increasing larger magnitudes.- Parameters:
x0
- Inclusive domain bound.x1
- Inclusive internal bound.- Returns:
P(x0 <= X <= x1)
.
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getMean
public double getMean()Gets the mean of this distribution.For population size \( N \), number of successes \( K \), and sample size \( n \), the mean is:
\[ n \frac{K}{N} \]
- Returns:
- the mean.
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getVariance
public double getVariance()Gets the variance of this distribution.For population size \( N \), number of successes \( K \), and sample size \( n \), the variance is:
\[ n \frac{K}{N} \frac{N-K}{N} \frac{N-n}{N-1} \]
- Returns:
- the variance.
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getSupportLowerBound
public int getSupportLowerBound()Gets the lower bound of the support. This method must return the same value asinverseCumulativeProbability(0)
, i.e. \( \inf \{ x \in \mathbb Z : P(X \le x) \gt 0 \} \). By convention,Integer.MIN_VALUE
should be substituted for negative infinity.For population size \( N \), number of successes \( K \), and sample size \( n \), the lower bound of the support is \( \max \{ 0, n + K - N \} \).
- Returns:
- lower bound of the support
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getSupportUpperBound
public int getSupportUpperBound()Gets the upper bound of the support. This method must return the same value asinverseCumulativeProbability(1)
, i.e. \( \inf \{ x \in \mathbb Z : P(X \le x) = 1 \} \). By convention,Integer.MAX_VALUE
should be substituted for positive infinity.For number of successes \( K \), and sample size \( n \), the upper bound of the support is \( \min \{ n, K \} \).
- Returns:
- upper bound of the support
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