Class HypergeometricDistribution
- java.lang.Object
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- org.apache.commons.statistics.distribution.HypergeometricDistribution
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- All Implemented Interfaces:
DiscreteDistribution
public final class HypergeometricDistribution extends Object
Implementation of the hypergeometric distribution.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.
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Nested Class Summary
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Nested classes/interfaces inherited from interface org.apache.commons.statistics.distribution.DiscreteDistribution
DiscreteDistribution.Sampler
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Method Summary
All Methods Static Methods Instance Methods Concrete Methods Modifier and Type Method Description DiscreteDistribution.SamplercreateSampler(org.apache.commons.rng.UniformRandomProvider rng)Creates a sampler.doublecumulativeProbability(int x)For a random variableXwhose values are distributed according to this distribution, this method returnsP(X <= x).doublegetMean()Gets the mean of this distribution.intgetNumberOfSuccesses()Gets the number of successes parameter of this distribution.intgetPopulationSize()Gets the population size parameter of this distribution.intgetSampleSize()Gets the sample size parameter of this distribution.intgetSupportLowerBound()Gets the lower bound of the support.intgetSupportUpperBound()Gets the upper bound of the support.doublegetVariance()Gets the variance of this distribution.intinverseCumulativeProbability(double p)Computes the quantile function of this distribution.intinverseSurvivalProbability(double p)Computes the inverse survival probability function of this distribution.doublelogProbability(int x)For a random variableXwhose values are distributed according to this distribution, this method returnslog(P(X = x)), wherelogis the natural logarithm.static HypergeometricDistributionof(int populationSize, int numberOfSuccesses, int sampleSize)Creates a hypergeometric distribution.doubleprobability(int x)For a random variableXwhose values are distributed according to this distribution, this method returnsP(X = x).doubleprobability(int x0, int x1)For a random variableXwhose values are distributed according to this distribution, this method returnsP(x0 < X <= x1).doublesurvivalProbability(int x)For a random variableXwhose values are distributed according to this distribution, this method returnsP(X > x).
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Method Detail
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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 <= 0ornumberOfSuccesses > populationSize, orsampleSize > populationSize.
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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 variableXwhose 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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probability
public double probability(int x0, int x1)
For a random variableXwhose values are distributed according to this distribution, this method returnsP(x0 < X <= x1). The default implementation uses the identityP(x0 < X <= x1) = P(X <= x1) - P(X <= x0)Special cases:
- returns
0.0ifx0 == x1; - returns
probability(x1)ifx0 + 1 == x1;
- Specified by:
probabilityin interfaceDiscreteDistribution- Parameters:
x0- Lower bound (exclusive).x1- Upper bound (inclusive).- Returns:
- the probability that a random variable with this distribution
takes a value between
x0andx1, excluding the lower and including the upper endpoint.
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logProbability
public double logProbability(int x)
For a random variableXwhose values are distributed according to this distribution, this method returnslog(P(X = x)), wherelogis 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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cumulativeProbability
public double cumulativeProbability(int x)
For a random variableXwhose 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 variableXwhose 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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inverseCumulativeProbability
public int inverseCumulativeProbability(double p)
Computes the quantile function of this distribution. For a random variableXdistributed according to this distribution, the returned value is:\[ x = \begin{cases} \inf \{ x \in \mathbb Z : P(X \le x) \ge p\} & \text{for } 0 \lt p \le 1 \\ \inf \{ x \in \mathbb Z : P(X \le x) \gt 0 \} & \text{for } p = 0 \end{cases} \]
If the result exceeds the range of the data type
int, thenInteger.MIN_VALUEorInteger.MAX_VALUEis returned. In this case the result ofcumulativeProbability(x)called using the returnedp-quantile may not compute the originalp.The default implementation returns:
DiscreteDistribution.getSupportLowerBound()forp = 0,DiscreteDistribution.getSupportUpperBound()forp = 1, or- the result of a binary search between the lower and upper bound using
cumulativeProbability(x). The bounds may be bracketed for efficiency.
- Specified by:
inverseCumulativeProbabilityin interfaceDiscreteDistribution- Parameters:
p- Cumulative probability.- Returns:
- the smallest
p-quantile of this distribution (largest 0-quantile forp = 0).
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inverseSurvivalProbability
public int inverseSurvivalProbability(double p)
Computes the inverse survival probability function of this distribution. For a random variableXdistributed according to this distribution, the returned value is:\[ x = \begin{cases} \inf \{ x \in \mathbb Z : P(X \gt x) \le p\} & \text{for } 0 \le p \lt 1 \\ \inf \{ x \in \mathbb Z : P(X \gt x) \lt 1 \} & \text{for } p = 1 \end{cases} \]
If the result exceeds the range of the data type
int, thenInteger.MIN_VALUEorInteger.MAX_VALUEis returned. In this case the result ofsurvivalProbability(x)called using the returned(1-p)-quantile may not compute the originalp.By default, this is defined as
inverseCumulativeProbability(1 - p), but the specific implementation may be more accurate.The default implementation returns:
DiscreteDistribution.getSupportLowerBound()forp = 1,DiscreteDistribution.getSupportUpperBound()forp = 0, or- the result of a binary search between the lower and upper bound using
survivalProbability(x). The bounds may be bracketed for efficiency.
- Specified by:
inverseSurvivalProbabilityin interfaceDiscreteDistribution- Parameters:
p- Cumulative probability.- Returns:
- the smallest
(1-p)-quantile of this distribution (largest 0-quantile forp = 1).
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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_VALUEshould 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_VALUEshould 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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createSampler
public DiscreteDistribution.Sampler createSampler(org.apache.commons.rng.UniformRandomProvider rng)
Creates a sampler.- Specified by:
createSamplerin interfaceDiscreteDistribution- Parameters:
rng- Generator of uniformly distributed numbers.- Returns:
- a sampler that produces random numbers according this distribution.
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