Class LogUniformDistribution

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:

  • Field Details

    • 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 Details

    • LogUniformDistribution

      private LogUniformDistribution(double lower, double upper)
      Parameters:
      lower - Lower bound of this distribution (inclusive).
      upper - Upper bound of this distribution (inclusive).

  • Method Details

    • 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:
      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:

      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:

      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.