Interface ContinuousDistribution
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- All Known Implementing Classes:
BetaDistribution,CauchyDistribution,ChiSquaredDistribution,ExponentialDistribution,FDistribution,FoldedNormalDistribution,GammaDistribution,GumbelDistribution,LaplaceDistribution,LevyDistribution,LogisticDistribution,LogNormalDistribution,LogUniformDistribution,NakagamiDistribution,NormalDistribution,ParetoDistribution,TDistribution,TrapezoidalDistribution,TriangularDistribution,TruncatedNormalDistribution,UniformContinuousDistribution,WeibullDistribution
public interface ContinuousDistribution
Interface for distributions on the reals.
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Nested Class Summary
Nested Classes Modifier and Type Interface Description static interfaceContinuousDistribution.SamplerDistribution sampling functionality.
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Method Summary
All Methods Instance Methods Abstract Methods Default Methods Modifier and Type Method Description ContinuousDistribution.SamplercreateSampler(org.apache.commons.rng.UniformRandomProvider rng)Creates a sampler.doublecumulativeProbability(double x)For a random variableXwhose values are distributed according to this distribution, this method returnsP(X <= x).doubledensity(double x)Returns the probability density function (PDF) of this distribution evaluated at the specified pointx.doublegetMean()Gets the mean of this distribution.doublegetSupportLowerBound()Gets the lower bound of the support.doublegetSupportUpperBound()Gets the upper bound of the support.doublegetVariance()Gets the variance of this distribution.doubleinverseCumulativeProbability(double p)Computes the quantile function of this distribution.default doubleinverseSurvivalProbability(double p)Computes the inverse survival probability function of this distribution.default doublelogDensity(double x)Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified pointx.default doubleprobability(double x0, double x1)For a random variableXwhose values are distributed according to this distribution, this method returnsP(x0 < X <= x1).default doublesurvivalProbability(double 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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density
double density(double x)
Returns the probability density function (PDF) of this distribution evaluated at the specified pointx. In general, the PDF is the derivative of the CDF. If the derivative does not exist atx, then an appropriate replacement should be returned, e.g.Double.POSITIVE_INFINITY,Double.NaN, or the limit inferior or limit superior of the difference quotient.- Parameters:
x- Point at which the PDF is evaluated.- Returns:
- the value of the probability density function at
x.
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probability
default double probability(double x0, double 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)- 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.
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logDensity
default double logDensity(double x)
Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified pointx.- Parameters:
x- Point at which the PDF is evaluated.- Returns:
- the logarithm of the value of the probability density function
at
x.
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cumulativeProbability
double cumulativeProbability(double 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(double 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
double inverseCumulativeProbability(double p)
Computes the quantile function of this distribution. For a random variableXdistributed according to this distribution, the returned value is:\[ x = \begin{cases} \inf \{ x \in \mathbb R : P(X \le x) \ge p\} & \text{for } 0 \lt p \le 1 \\ \inf \{ x \in \mathbb R : P(X \le x) \gt 0 \} & \text{for } p = 0 \end{cases} \]
- 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 double inverseSurvivalProbability(double p)
Computes the inverse survival probability function of this distribution. For a random variableXdistributed according to this distribution, the returned value is:\[ x = \begin{cases} \inf \{ x \in \mathbb R : P(X \gt x) \le p\} & \text{for } 0 \le p \lt 1 \\ \inf \{ x \in \mathbb R : P(X \gt x) \lt 1 \} & \text{for } p = 1 \end{cases} \]
By default, this is defined as
inverseCumulativeProbability(1 - p), but the specific implementation may be more accurate.- Parameters:
p- Survival 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
double getSupportLowerBound()
Gets the lower bound of the support. It must return the same value asinverseCumulativeProbability(0), i.e. \( \inf \{ x \in \mathbb R : P(X \le x) \gt 0 \} \).- Returns:
- the lower bound of the support.
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getSupportUpperBound
double getSupportUpperBound()
Gets the upper bound of the support. It must return the same value asinverseCumulativeProbability(1), i.e. \( \inf \{ x \in \mathbb R : P(X \le x) = 1 \} \).- Returns:
- the upper bound of the support.
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createSampler
ContinuousDistribution.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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