Class LogUniformDistribution
- java.lang.Object
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- org.apache.commons.statistics.distribution.AbstractContinuousDistribution
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- org.apache.commons.statistics.distribution.LogUniformDistribution
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- All Implemented Interfaces:
ContinuousDistribution
public final class LogUniformDistribution extends AbstractContinuousDistribution
Implementation of the log-uniform distribution. This is also known as the reciprocal distribution.The probability density function of \( X \) is:
\[ f(x; a, b) = \frac{1}{x \ln \frac b a} \]
for \( 0 \lt a \lt b \lt \infty \) and \( x \in [a, b] \).
- Since:
- 1.1
- See Also:
- Reciprocal distribution (Wikipedia)
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Nested Class Summary
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Nested classes/interfaces inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution
ContinuousDistribution.Sampler
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Field Summary
Fields Modifier and Type Field Description private double
logA
log(a).private double
logB
log(b).private double
logBmLogA
log(b) - log(a).private double
logLogBmLogA
log(log(b) - log(a)).private double
lower
Lower bound (a) of this distribution (inclusive).private double
upper
Upper bound (b) of this distribution (exclusive).
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Constructor Summary
Constructors Modifier Constructor Description private
LogUniformDistribution(double lower, double upper)
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Method Summary
All Methods Static Methods Instance Methods Concrete Methods Modifier and Type Method Description private static double
clip(double x, double lower, double upper)
Clip the value to the range [lower, upper].private double
clipToRange(double x)
Clip the value to the range [lower, upper].ContinuousDistribution.Sampler
createSampler(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.(package private) double
getMedian()
Gets the median.double
getSupportLowerBound()
Gets the lower bound of the support.double
getSupportUpperBound()
Gets the upper bound of the support.double
getVariance()
Gets the variance of this distribution.double
inverseCumulativeProbability(double p)
Computes the quantile function of this distribution.double
inverseSurvivalProbability(double p)
Computes the inverse survival probability function of this distribution.double
logDensity(double x)
Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified pointx
.static LogUniformDistribution
of(double lower, double upper)
Creates a log-uniform distribution.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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Methods inherited from class org.apache.commons.statistics.distribution.AbstractContinuousDistribution
isSupportConnected, probability
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Field Detail
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lower
private final double lower
Lower bound (a) of this distribution (inclusive).
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upper
private final double upper
Upper bound (b) of this distribution (exclusive).
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logA
private final double logA
log(a).
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logB
private final double logB
log(b).
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logBmLogA
private final double logBmLogA
log(b) - log(a).
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logLogBmLogA
private final double logLogBmLogA
log(log(b) - log(a)).
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Method Detail
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of
public static LogUniformDistribution of(double lower, double upper)
Creates a log-uniform distribution.- Parameters:
lower
- Lower bound of this distribution (inclusive).upper
- Upper bound of this distribution (inclusive).- Returns:
- the distribution
- Throws:
java.lang.IllegalArgumentException
- iflower >= upper
; the range between the bounds is not finite; orlower <= 0
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density
public 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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logDensity
public 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
public 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
public 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
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
- Overrides:
inverseCumulativeProbability
in classAbstractContinuousDistribution
- Parameters:
p
- Cumulative probability.- Returns:
- the smallest
p
-quantile of this distribution (largest 0-quantile forp = 0
).
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inverseSurvivalProbability
public double inverseSurvivalProbability(double p)
Description copied from class:AbstractContinuousDistribution
Computes the inverse survival probability function of this distribution. For a random variableX
distributed according to this distribution, the returned value is:\[ x = \begin{cases} \inf \{ x \in \mathbb R : P(X \gt x) \le p\} & \text{for } 0 \le p \lt 1 \\ \inf \{ x \in \mathbb R : P(X \gt x) \lt 1 \} & \text{for } p = 1 \end{cases} \]
By default, this is defined as
inverseCumulativeProbability(1 - p)
, but the specific implementation may be more accurate.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
- Overrides:
inverseSurvivalProbability
in classAbstractContinuousDistribution
- Parameters:
p
- Survival probability.- Returns:
- the smallest
(1-p)
-quantile of this distribution (largest 0-quantile forp = 1
).
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getMean
public double getMean()
Gets the mean of this distribution.For lower bound \( a \) and upper bound \( b \), the mean is:
\[ \frac{b - a}{\ln \frac b a} \]
- Returns:
- the mean.
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getVariance
public double getVariance()
Gets the variance of this distribution.For lower bound \( a \) and upper bound \( b \), the variance is:
\[ \frac{b^2 - a^2}{2 \ln \frac b a} - \left( \frac{b - a}{\ln \frac b a} \right)^2 \]
- Returns:
- the variance.
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getSupportLowerBound
public double getSupportLowerBound()
Gets the lower bound of the support. It must return the same value asinverseCumulativeProbability(0)
, i.e. \( \inf \{ x \in \mathbb R : P(X \le x) \gt 0 \} \).The lower bound of the support is equal to the lower bound parameter of the distribution.
- Returns:
- the lower bound of the support.
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getSupportUpperBound
public double getSupportUpperBound()
Gets the upper bound of the support. It must return the same value asinverseCumulativeProbability(1)
, i.e. \( \inf \{ x \in \mathbb R : P(X \le x) = 1 \} \).The upper bound of the support is equal to the upper bound parameter of the distribution.
- Returns:
- the upper bound of the support.
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clipToRange
private double clipToRange(double x)
Clip the value to the range [lower, upper]. This is used to handle floating-point error at the support bound.- Parameters:
x
- Value x- Returns:
- x clipped to the range
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clip
private static double clip(double x, double lower, double upper)
Clip the value to the range [lower, upper].- Parameters:
x
- Value xlower
- Lower bound (inclusive)upper
- Upper bound (inclusive)- Returns:
- x clipped to the range
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getMedian
double getMedian()
Gets the median. This is used to determine if the arguments to theAbstractContinuousDistribution.probability(double, double)
function are in the upper or lower domain.The default implementation calls
AbstractContinuousDistribution.inverseCumulativeProbability(double)
with a value of 0.5.- Overrides:
getMedian
in classAbstractContinuousDistribution
- Returns:
- the median
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createSampler
public ContinuousDistribution.Sampler createSampler(org.apache.commons.rng.UniformRandomProvider rng)
Creates a sampler.- Specified by:
createSampler
in interfaceContinuousDistribution
- Overrides:
createSampler
in classAbstractContinuousDistribution
- Parameters:
rng
- Generator of uniformly distributed numbers.- Returns:
- a sampler that produces random numbers according this distribution.
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