Interface DiscreteDistribution
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- All Known Implementing Classes:
BinomialDistribution,GeometricDistribution,HypergeometricDistribution,PascalDistribution,PoissonDistribution,UniformDiscreteDistribution,ZipfDistribution
public interface DiscreteDistribution
Interface for distributions on the integers.
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Nested Class Summary
Nested Classes Modifier and Type Interface Description static interfaceDiscreteDistribution.SamplerDistribution sampling functionality.
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Method Summary
All Methods Instance Methods Abstract Methods Default 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.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.default intinverseSurvivalProbability(double p)Computes the inverse survival probability function of this distribution.default doublelogProbability(int x)For a random variableXwhose values are distributed according to this distribution, this method returnslog(P(X = x)), wherelogis the natural logarithm.doubleprobability(int x)For a random variableXwhose values are distributed according to this distribution, this method returnsP(X = x).default doubleprobability(int x0, int x1)For a random variableXwhose values are distributed according to this distribution, this method returnsP(x0 < X <= x1).default 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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probability
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
default 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;
- 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. - Throws:
IllegalArgumentException- ifx0 > x1.
- returns
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logProbability
default 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
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
default 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
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.- Parameters:
p- Cumulative probability.- Returns:
- the smallest
p-quantile of this distribution (largest 0-quantile forp = 0). - Throws:
IllegalArgumentException- ifp < 0orp > 1.
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inverseSurvivalProbability
default 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.- Parameters:
p- Cumulative probability.- Returns:
- the smallest
(1-p)-quantile of this distribution (largest 0-quantile forp = 1). - Throws:
IllegalArgumentException- ifp < 0orp > 1.
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getMean
double getMean()
Gets the mean of this distribution.- Returns:
- the mean.
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getVariance
double getVariance()
Gets the variance of this distribution.- Returns:
- the variance.
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getSupportLowerBound
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.- Returns:
- the lower bound of the support.
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getSupportUpperBound
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.- Returns:
- the upper bound of the support.
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createSampler
DiscreteDistribution.Sampler createSampler(org.apache.commons.rng.UniformRandomProvider rng)
Creates a sampler.- Parameters:
rng- Generator of uniformly distributed numbers.- Returns:
- a sampler that produces random numbers according this distribution.
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