Class BinomialDistribution
- All Implemented Interfaces:
DiscreteDistribution
The probability mass function of \( X \) is:
\[ f(k; n, p) = \binom{n}{k} p^k (1-p)^{n-k} \]
for \( n \in \{0, 1, 2, \dots\} \) the number of trials, \( p \in [0, 1] \) the probability of success, \( k \in \{0, 1, \dots, n\} \) the number of successes, and
\[ \binom{n}{k} = \frac{n!}{k! \, (n-k)!} \]
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 static final float
1/2.private final int
The number of trials.private final double
Cached value for pmf(x=0).private final double
Cached value for pmf(x=n).private final double
The probability of success. -
Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptiondouble
cumulativeProbability
(int x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X <= x)
.double
getMean()
Gets the mean of this distribution.(package private) int
Gets the median.int
Gets the number of trials parameter of this distribution.double
Gets the probability of success parameter of this distribution.int
Gets the lower bound of the support.int
Gets the upper bound of the support.double
Gets the variance of this distribution.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 BinomialDistribution
of
(int trials, double p) Creates a binomial 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, inverseCumulativeProbability, inverseSurvivalProbability, probability
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Field Details
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HALF
private static final float HALF1/2.- See Also:
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numberOfTrials
private final int numberOfTrialsThe number of trials. -
probabilityOfSuccess
private final double probabilityOfSuccessThe probability of success. -
pmf0
private final double pmf0Cached value for pmf(x=0). -
pmfn
private final double pmfnCached value for pmf(x=n).
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Constructor Details
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BinomialDistribution
private BinomialDistribution(int trials, double p) - Parameters:
trials
- Number of trials.p
- Probability of success.
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Method Details
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of
Creates a binomial distribution.- Parameters:
trials
- Number of trials.p
- Probability of success.- Returns:
- the distribution
- Throws:
IllegalArgumentException
- iftrials < 0
, or ifp < 0
orp > 1
.
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getNumberOfTrials
public int getNumberOfTrials()Gets the number of trials parameter of this distribution.- Returns:
- the number of trials.
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getProbabilityOfSuccess
public double getProbabilityOfSuccess()Gets the probability of success parameter of this distribution.- Returns:
- the probability of success.
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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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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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getMean
public double getMean()Gets the mean of this distribution.For number of trials \( n \) and probability of success \( p \), the mean is \( np \).
- Returns:
- the mean.
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getVariance
public double getVariance()Gets the variance of this distribution.For number of trials \( n \) and probability of success \( p \), the variance is \( np (1 - p) \).
- 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.The lower bound of the support is always 0 except for the probability parameter
p = 1
.- Returns:
- 0 or the number of trials.
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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.The upper bound of the support is the number of trials except for the probability parameter
p = 0
.- Returns:
- number of trials or 0.
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getMedian
int getMedian()Gets the median. This is used to determine if the arguments to theAbstractDiscreteDistribution.probability(int, int)
function are in the upper or lower domain.The default implementation calls
AbstractDiscreteDistribution.inverseCumulativeProbability(double)
with a value of 0.5.- Overrides:
getMedian
in classAbstractDiscreteDistribution
- Returns:
- the median
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