Class AbstractContinuousDistribution
- All Implemented Interfaces:
ContinuousDistribution
- Direct Known Subclasses:
BetaDistribution
,CauchyDistribution
,ChiSquaredDistribution
,ExponentialDistribution
,FDistribution
,GammaDistribution
,GumbelDistribution
,LaplaceDistribution
,LevyDistribution
,LogisticDistribution
,LogNormalDistribution
,NakagamiDistribution
,NormalDistribution
,ParetoDistribution
,TDistribution
,TrapezoidalDistribution
,TriangularDistribution
,TruncatedNormalDistribution
,UniformContinuousDistribution
,WeibullDistribution
This base class provides a default factory method for creating
a sampler instance
that uses the
inversion method for generating random samples that follow the
distribution.
The class provides functionality to evaluate the probability in a range
using either the cumulative probability or the survival probability.
The survival probability is used if both arguments to
probability(double, double)
are above the median.
Child classes with a known median can override the default getMedian()
method.
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Nested Class Summary
Nested classes/interfaces inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution
ContinuousDistribution.Sampler
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Field Summary
FieldsModifier and TypeFieldDescriptionprivate double
Cached value of the median.private static final double
BrentSolver absolute accuracy.private static final double
BrentSolver function value accuracy.private static final double
BrentSolver relative accuracy. -
Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptionprivate double
createFiniteLowerBound
(double p, double q, boolean complement, double upperBound, double mu, double sig, boolean chebyshevApplies) Create a finite lower bound.private double
createFiniteUpperBound
(double p, double q, boolean complement, double lowerBound, double mu, double sig, boolean chebyshevApplies) Create a finite upper bound.createSampler
(org.apache.commons.rng.UniformRandomProvider rng) Creates a sampler.(package private) double
Gets the median.double
inverseCumulativeProbability
(double p) Computes the quantile function of this distribution.private double
inverseProbability
(double p, double q, boolean complement) Implementation for the inverse cumulative or survival probability.double
inverseSurvivalProbability
(double p) Computes the inverse survival probability function of this distribution.(package private) boolean
Indicates whether the support is connected, i.e.double
probability
(double x0, double x1) For a random variableX
whose values are distributed according to this distribution, this method returnsP(x0 < X <= x1)
.private double
searchPlateau
(boolean complement, double lower, double x) Test the probability function for a plateau at the point x.Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
Methods inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution
cumulativeProbability, density, getMean, getSupportLowerBound, getSupportUpperBound, getVariance, logDensity, survivalProbability
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Field Details
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SOLVER_RELATIVE_ACCURACY
private static final double SOLVER_RELATIVE_ACCURACYBrentSolver relative accuracy. This is used withtol = 2 * relEps * abs(b) + absEps
so the minimum non-zero value with an effect is half of machine epsilon (2^-53).- See Also:
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SOLVER_ABSOLUTE_ACCURACY
private static final double SOLVER_ABSOLUTE_ACCURACYBrentSolver absolute accuracy. This is used withtol = 2 * relEps * abs(b) + absEps
so set to MIN_VALUE so that when the relative epsilon has no effect (as b is too small) the tolerance is at least 1 ULP for sub-normal numbers.- See Also:
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SOLVER_FUNCTION_VALUE_ACCURACY
private static final double SOLVER_FUNCTION_VALUE_ACCURACYBrentSolver function value accuracy. Determines if the Brent solver performs a search. It is not used during the search. Set to a very low value to search using Brent's method unless the starting point is correct, or within 1 ULP for sub-normal probabilities.- See Also:
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median
private double medianCached value of the median.
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Constructor Details
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AbstractContinuousDistribution
AbstractContinuousDistribution()
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Method Details
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getMedian
double getMedian()Gets the median. This is used to determine if the arguments to theprobability(double, double)
function are in the upper or lower domain.The default implementation calls
inverseCumulativeProbability(double)
with a value of 0.5.- Returns:
- the median
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probability
public 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)
- Specified by:
probability
in interfaceContinuousDistribution
- 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.
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inverseCumulativeProbability
public double inverseCumulativeProbability(double p) Computes the quantile function of this distribution. For a random variableX
distributed according to this distribution, the returned value is:\[ x = \begin{cases} \inf \{ x \in \mathbb R : P(X \le x) \ge p\} & \text{for } 0 \lt p \le 1 \\ \inf \{ x \in \mathbb R : P(X \le x) \gt 0 \} & \text{for } p = 0 \end{cases} \]
The default implementation returns:
ContinuousDistribution.getSupportLowerBound()
forp = 0
,ContinuousDistribution.getSupportUpperBound()
forp = 1
, or- the result of a search for a root between the lower and upper bound using
cumulativeProbability(x) - p
. The bounds may be bracketed for efficiency.
- Specified by:
inverseCumulativeProbability
in interfaceContinuousDistribution
- 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
public 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.The default implementation returns:
ContinuousDistribution.getSupportLowerBound()
forp = 1
,ContinuousDistribution.getSupportUpperBound()
forp = 0
, or- the result of a search for a root between the lower and upper bound using
survivalProbability(x) - p
. The bounds may be bracketed for efficiency.
- Specified by:
inverseSurvivalProbability
in interfaceContinuousDistribution
- 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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inverseProbability
private double inverseProbability(double p, double q, boolean complement) Implementation for the inverse cumulative or survival probability.- Parameters:
p
- Cumulative probability.q
- Survival probability.complement
- Set to true to compute the inverse survival probability- Returns:
- the value
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createFiniteLowerBound
private double createFiniteLowerBound(double p, double q, boolean complement, double upperBound, double mu, double sig, boolean chebyshevApplies) Create a finite lower bound. Assumes the current lower bound is negative infinity.- Parameters:
p
- Cumulative probability.q
- Survival probability.complement
- Set to true to compute the inverse survival probabilityupperBound
- Current upper boundmu
- Meansig
- Standard deviationchebyshevApplies
- True if the Chebyshev inequality applies (mean is finite andsig > 0
}- Returns:
- the finite lower bound
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createFiniteUpperBound
private double createFiniteUpperBound(double p, double q, boolean complement, double lowerBound, double mu, double sig, boolean chebyshevApplies) Create a finite upper bound. Assumes the current upper bound is positive infinity.- Parameters:
p
- Cumulative probability.q
- Survival probability.complement
- Set to true to compute the inverse survival probabilitylowerBound
- Current lower boundmu
- Meansig
- Standard deviationchebyshevApplies
- True if the Chebyshev inequality applies (mean is finite andsig > 0
}- Returns:
- the finite lower bound
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isSupportConnected
boolean isSupportConnected()Indicates whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support.This method is used in the default implementation of the inverse cumulative and survival probability functions.
The default value is true which assumes the cdf and sf have no plateau regions where the same probability value is returned for a large range of x. Override this method if there are gaps in the support of the cdf and sf.
If false then the inverse will perform an additional step to ensure that the lower-bound of the interval on which the cdf is constant should be returned. This will search from the initial point x downwards if a smaller value also has the same cumulative (survival) probability.
Any plateau with a width in x smaller than the inverse absolute accuracy will not be searched.
Note: This method was public in commons math. It has been reduced to package private in commons statistics as it is an implementation detail.
- Returns:
- whether the support is connected.
- See Also:
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searchPlateau
private double searchPlateau(boolean complement, double lower, double x) Test the probability function for a plateau at the point x. If detected search the plateau for the lowest point y such thatinf{y in R | P(y) == P(x)}
.This function is used when the distribution support is not connected to satisfy the inverse probability requirements of
ContinuousDistribution
on the returned value.- Parameters:
complement
- Set to true to search the survival probability.lower
- Lower bound used to limit the search downwards.x
- Current value.- Returns:
- the infimum y
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createSampler
public ContinuousDistribution.Sampler createSampler(org.apache.commons.rng.UniformRandomProvider rng) Creates a sampler.- Specified by:
createSampler
in interfaceContinuousDistribution
- Parameters:
rng
- Generator of uniformly distributed numbers.- Returns:
- a sampler that produces random numbers according this distribution.
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