Class LaplaceDistribution

    • Field Summary

      Fields 
      Modifier and Type Field Description
      private double beta
      The scale parameter.
      private double log2beta
      log(2 * beta).
      private double mu
      The location parameter.
    • Constructor Summary

      Constructors 
      Modifier Constructor Description
      private LaplaceDistribution​(double mu, double beta)  
    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      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 getLocation()
      Gets the location parameter of this distribution.
      double getMean()
      Gets the mean of this distribution.
      (package private) double getMedian()
      Gets the median.
      double getScale()
      Gets the scale parameter of this distribution.
      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 LaplaceDistribution of​(double mu, double beta)
      Creates a Laplace 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

      • mu

        private final double mu
        The location parameter.
      • beta

        private final double beta
        The scale parameter.
      • log2beta

        private final double log2beta
        log(2 * beta).
    • Constructor Detail

      • LaplaceDistribution

        private LaplaceDistribution​(double mu,
                                    double beta)
        Parameters:
        mu - Location parameter.
        beta - Scale parameter (must be positive).
    • Method Detail

      • of

        public static LaplaceDistribution of​(double mu,
                                             double beta)
        Creates a Laplace distribution.
        Parameters:
        mu - Location parameter.
        beta - Scale parameter (must be positive).
        Returns:
        the distribution
        Throws:
        java.lang.IllegalArgumentException - if beta <= 0
      • getLocation

        public double getLocation()
        Gets the location parameter of this distribution.
        Returns:
        the location parameter.
      • getScale

        public double getScale()
        Gets the scale parameter of this distribution.
        Returns:
        the scale parameter.
      • 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.
      • inverseSurvivalProbability

        public double inverseSurvivalProbability​(double p)
        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.

        The mean is equal to the location.

        Returns:
        the mean.
      • getVariance

        public double getVariance()
        Gets the variance of this distribution.

        For scale parameter \( b \), the variance is \( 2 b^2 \).

        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 always negative infinity.

        Returns:
        negative infinity.
      • 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 always positive infinity.

        Returns:
        positive infinity.