java.lang.Object
- org.apache.commons.statistics.distribution.AbstractContinuousDistribution
- - org.apache.commons.statistics.distribution.LogUniformDistribution

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)

Nested Class Summary
- Nested classes/interfaces inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution
  ContinuousDistribution.Sampler

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).

Constructor Summary

Constructors
Modifier Constructor Description

private LogUniformDistribution(double lower, double upper)

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 variable `X` whose values are distributed according to this distribution, this method returns `P(X <= x)`.
`double`	`density(double x)`	Returns the probability density function (PDF) of this distribution evaluated at the specified point `x`.
`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 point `x`.
`static LogUniformDistribution`	`of(double lower, double upper)`	Creates a log-uniform distribution.
`double`	`survivalProbability(double x)`	For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X > x)`.

Methods inherited from class org.apache.commons.statistics.distribution.AbstractContinuousDistribution
isSupportConnected, probability

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - lower
```
private final double lower
```
    Lower bound (a) of this distribution (inclusive).
  - upper
```
private final double upper
```
    Upper bound (b) of this distribution (exclusive).
  - logA
```
private final double logA
```
    log(a).
  - logB
```
private final double logB
```
    log(b).
  - logBmLogA
```
private final double logBmLogA
```
    log(b) - log(a).
  - logLogBmLogA
```
private final double logLogBmLogA
```
    log(log(b) - log(a)).
- Constructor Detail
  - LogUniformDistribution
```
private LogUniformDistribution(double lower,
                               double upper)
```
    Parameters:
    
    lower - Lower bound of this distribution (inclusive).
    
    upper - Upper bound of this distribution (inclusive).
- Method Detail
  - 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 - if lower >= upper; the range between the bounds is not finite; or lower <= 0
  - density
```
public double density(double x)
```
    Returns the probability density function (PDF) of this distribution evaluated at the specified point x. In general, the PDF is the derivative of the CDF. If the derivative does not exist at x, 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.
  - logDensity
```
public double logDensity(double x)
```
    Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x.
    
    Parameters:
    
    x - Point at which the PDF is evaluated.
    
    Returns:
    
    the logarithm of the value of the probability density function at x.
  - cumulativeProbability
```
public double cumulativeProbability(double x)
```
    For a random variable X whose values are distributed according to this distribution, this method returns P(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.
  - survivalProbability
```
public double survivalProbability(double x)
```
    For a random variable X whose values are distributed according to this distribution, this method returns P(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.
  - inverseCumulativeProbability
```
public double inverseCumulativeProbability(double p)
```
    Computes the quantile function of this distribution. For a random variable X 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() for p = 0,
    
    ContinuousDistribution.getSupportUpperBound() for p = 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 interface ContinuousDistribution
    
    Overrides:
    
    inverseCumulativeProbability in class AbstractContinuousDistribution
    
    Parameters:
    
    p - Cumulative probability.
    
    Returns:
    
    the smallest p-quantile of this distribution (largest 0-quantile for p = 0).
  - inverseSurvivalProbability
```
public double inverseSurvivalProbability(double p)
```
    Description copied from class: AbstractContinuousDistribution
    Computes the inverse survival probability function of this distribution. For a random variable X 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() for p = 1,
    
    ContinuousDistribution.getSupportUpperBound() for p = 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 interface ContinuousDistribution
    
    Overrides:
    
    inverseSurvivalProbability in class AbstractContinuousDistribution
    
    Parameters:
    
    p - Survival probability.
    
    Returns:
    
    the smallest (1-p)-quantile of this distribution (largest 0-quantile for p = 1).
  - 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.
  - 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.
  - getSupportLowerBound
```
public double getSupportLowerBound()
```
    Gets the lower bound of the support. It must return the same value as inverseCumulativeProbability(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.
  - getSupportUpperBound
```
public double getSupportUpperBound()
```
    Gets the upper bound of the support. It must return the same value as inverseCumulativeProbability(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.
  - 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
  - clip
```
private static double clip(double x,
                           double lower,
                           double upper)
```
    Clip the value to the range [lower, upper].
    
    Parameters:
    
    x - Value x
    
    lower - Lower bound (inclusive)
    
    upper - Upper bound (inclusive)
    
    Returns:
    
    x clipped to the range
  - getMedian
```
double getMedian()
```
    Gets the median. This is used to determine if the arguments to the AbstractContinuousDistribution.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 class AbstractContinuousDistribution
    
    Returns:
    
    the median
  - createSampler
```
public ContinuousDistribution.Sampler createSampler(org.apache.commons.rng.UniformRandomProvider rng)
```
    Creates a sampler.
    
    Specified by:
    
    createSampler in interface ContinuousDistribution
    
    Overrides:
    
    createSampler in class AbstractContinuousDistribution
    
    Parameters:
    
    rng - Generator of uniformly distributed numbers.
    
    Returns:
    
    a sampler that produces random numbers according this distribution.

Class LogUniformDistribution

Nested Class Summary

Nested classes/interfaces inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution

Field Summary

Constructor Summary

Method Summary

Methods inherited from class org.apache.commons.statistics.distribution.AbstractContinuousDistribution

Methods inherited from class java.lang.Object

Field Detail

lower

upper

logA

logB

logBmLogA

logLogBmLogA

Constructor Detail

LogUniformDistribution

Method Detail

of

density

logDensity

cumulativeProbability

survivalProbability

inverseCumulativeProbability

inverseSurvivalProbability

getMean

getVariance

getSupportLowerBound

getSupportUpperBound

clipToRange

clip

getMedian

createSampler