Class 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)
    • 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 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.
      • 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