Interface ContinuousDistribution
- All Known Implementing Classes:
AbstractContinuousDistribution
,BetaDistribution
,CauchyDistribution
,ChiSquaredDistribution
,ExponentialDistribution
,FDistribution
,GammaDistribution
,GumbelDistribution
,LaplaceDistribution
,LevyDistribution
,LogisticDistribution
,LogNormalDistribution
,NakagamiDistribution
,NormalDistribution
,ParetoDistribution
,TDistribution
,TDistribution.NormalTDistribution
,TDistribution.StudentsTDistribution
,TrapezoidalDistribution
,TrapezoidalDistribution.DelegatedTrapezoidalDistribution
,TrapezoidalDistribution.RegularTrapezoidalDistribution
,TrapezoidalDistribution.TriangularTrapezoidalDistribution
,TrapezoidalDistribution.UniformTrapezoidalDistribution
,TriangularDistribution
,TruncatedNormalDistribution
,UniformContinuousDistribution
,WeibullDistribution
public interface ContinuousDistribution
Interface for distributions on the reals.
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Nested Class Summary
Nested ClassesModifier and TypeInterfaceDescriptionstatic interface
Distribution sampling functionality. -
Method Summary
Modifier and TypeMethodDescriptioncreateSampler
(org.apache.commons.rng.UniformRandomProvider rng) Creates a sampler.double
cumulativeProbability
(double x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X <= x)
.double
density
(double x) Returns the probability density function (PDF) of this distribution evaluated at the specified pointx
.double
getMean()
Gets the mean of this distribution.double
Gets the lower bound of the support.double
Gets the upper bound of the support.double
Gets the variance of this distribution.double
inverseCumulativeProbability
(double p) Computes the quantile function of this distribution.default double
inverseSurvivalProbability
(double p) Computes the inverse survival probability function of this distribution.default double
logDensity
(double x) Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified pointx
.default double
probability
(double x0, double x1) For a random variableX
whose values are distributed according to this distribution, this method returnsP(x0 < X <= x1)
.default double
survivalProbability
(double x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X > x)
.
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Method Details
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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 theCDF
. 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 variableX
whose 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
x0
andx1
, 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 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
default double survivalProbability(double 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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inverseCumulativeProbability
double inverseCumulativeProbability(double p) Computes the quantile function of this distribution. For a random variableX
distributed 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 < 0
orp > 1
.
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inverseSurvivalProbability
default double inverseSurvivalProbability(double p) Computes the inverse survival probability function of this distribution. For a random variableX
distributed according to this distribution, the returned value is:\[ x = \begin{cases} \inf \{ x \in \mathbb R : P(X \ge x) \le p\} & \text{for } 0 \le p \lt 1 \\ \inf \{ x \in \mathbb R : P(X \ge x) \lt 1 \} & \text{for } p = 1 \end{cases} \]
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 < 0
orp > 1
.
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getMean
double getMean()Gets the mean of this distribution.- Returns:
- the mean.
-
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
Creates a sampler.- Parameters:
rng
- Generator of uniformly distributed numbers.- Returns:
- a sampler that produces random numbers according this distribution.
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