public final class HypergeometricDistribution extends Object
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.
DiscreteDistribution.Sampler
Modifier and Type | Method and Description |
---|---|
DiscreteDistribution.Sampler |
createSampler(UniformRandomProvider rng)
Creates a sampler.
|
double |
cumulativeProbability(int x)
For a random variable
X whose values are distributed according
to this distribution, this method returns P(X <= x) . |
double |
getMean()
Gets the mean of this distribution.
|
int |
getNumberOfSuccesses()
Gets the number of successes parameter of this distribution.
|
int |
getPopulationSize()
Gets the population size parameter of this distribution.
|
int |
getSampleSize()
Gets the sample size parameter of this distribution.
|
int |
getSupportLowerBound()
Gets the lower bound of the support.
|
int |
getSupportUpperBound()
Gets the upper bound of the support.
|
double |
getVariance()
Gets the variance of this distribution.
|
int |
inverseCumulativeProbability(double p)
Computes the quantile function of this distribution.
|
int |
inverseSurvivalProbability(double p)
Computes the inverse survival probability function of this distribution.
|
double |
logProbability(int x)
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. |
static HypergeometricDistribution |
of(int populationSize,
int numberOfSuccesses,
int sampleSize)
Creates a hypergeometric distribution.
|
double |
probability(int x)
For a random variable
X whose values are distributed according
to this distribution, this method returns P(X = x) . |
double |
probability(int x0,
int x1)
For a random variable
X whose values are distributed according
to this distribution, this method returns P(x0 < X <= x1) . |
double |
survivalProbability(int x)
For a random variable
X whose values are distributed according
to this distribution, this method returns P(X > x) . |
public static HypergeometricDistribution of(int populationSize, int numberOfSuccesses, int sampleSize)
populationSize
- Population size.numberOfSuccesses
- Number of successes in the population.sampleSize
- Sample size.IllegalArgumentException
- if numberOfSuccesses < 0
, or
populationSize <= 0
or numberOfSuccesses > populationSize
, or
sampleSize > populationSize
.public int getPopulationSize()
public int getNumberOfSuccesses()
public int getSampleSize()
public double probability(int x)
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.x
- Point at which the PMF is evaluated.x
.public double logProbability(int x)
X
whose values are distributed according
to this distribution, this method returns log(P(X = x))
, where
log
is the natural logarithm.x
- Point at which the PMF is evaluated.x
.public double cumulativeProbability(int x)
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.x
- Point at which the CDF is evaluated.x
.public double survivalProbability(int x)
X
whose values are distributed according
to this distribution, this method returns P(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.
x
- Point at which the survival function is evaluated.x
.public double getMean()
For population size \( N \), number of successes \( K \), and sample size \( n \), the mean is:
\[ n \frac{K}{N} \]
public double getVariance()
For population size \( N \), number of successes \( K \), and sample size \( n \), the variance is:
\[ n \frac{K}{N} \frac{N-K}{N} \frac{N-n}{N-1} \]
public int getSupportLowerBound()
inverseCumulativeProbability(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 \( \max \{ 0, n + K - N \} \).
public int getSupportUpperBound()
inverseCumulativeProbability(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 \( \min \{ n, K \} \).
public double probability(int x0, int x1)
X
whose values are distributed according
to this distribution, this method returns P(x0 < X <= x1)
.
The default implementation uses the identity
P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)
Special cases:
0.0
if x0 == x1
;
probability(x1)
if x0 + 1 == x1
;
probability
in interface DiscreteDistribution
x0
- Lower bound (exclusive).x1
- Upper bound (inclusive).x0
and x1
, excluding the lower
and including the upper endpoint.public int inverseCumulativeProbability(double p)
X
distributed 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
,
then Integer.MIN_VALUE
or Integer.MAX_VALUE
is returned.
In this case the result of cumulativeProbability(x)
called using the returned p
-quantile may not compute the original p
.
The default implementation returns:
DiscreteDistribution.getSupportLowerBound()
for p = 0
,DiscreteDistribution.getSupportUpperBound()
for p = 1
, orcumulativeProbability(x)
.
The bounds may be bracketed for efficiency.inverseCumulativeProbability
in interface DiscreteDistribution
p
- Cumulative probability.p
-quantile of this distribution
(largest 0-quantile for p = 0
).IllegalArgumentException
- if p < 0
or p > 1
public int inverseSurvivalProbability(double p)
X
distributed according to this distribution,
the returned value is:
\[ x = \begin{cases} \inf \{ x \in \mathbb Z : P(X \ge x) \le p\} & \text{for } 0 \le p \lt 1 \\ \inf \{ x \in \mathbb Z : P(X \ge x) \lt 1 \} & \text{for } p = 1 \end{cases} \]
If the result exceeds the range of the data type int
,
then Integer.MIN_VALUE
or Integer.MAX_VALUE
is returned.
In this case the result of survivalProbability(x)
called using the returned (1-p)
-quantile may not compute the original p
.
By default, this is defined as inverseCumulativeProbability(1 - p)
, but
the specific implementation may be more accurate.
The default implementation returns:
DiscreteDistribution.getSupportLowerBound()
for p = 1
,DiscreteDistribution.getSupportUpperBound()
for p = 0
, orsurvivalProbability(x)
.
The bounds may be bracketed for efficiency.inverseSurvivalProbability
in interface DiscreteDistribution
p
- Cumulative probability.(1-p)
-quantile of this distribution
(largest 0-quantile for p = 1
).IllegalArgumentException
- if p < 0
or p > 1
public DiscreteDistribution.Sampler createSampler(UniformRandomProvider rng)
createSampler
in interface DiscreteDistribution
rng
- Generator of uniformly distributed numbers.Copyright © 2018–2022 The Apache Software Foundation. All rights reserved.