Class TriangularDistribution

    • Field Summary

      Fields 
      Modifier and Type Field Description
      private double a
      Lower limit of this distribution (inclusive).
      private double b
      Upper limit of this distribution (inclusive).
      private double c
      Mode of this distribution.
      private double cdfMode
      Cumulative probability at the mode.
      private double divisor1
      Cached value ((b - a) * (c - a).
      private double divisor2
      Cached value ((b - a) * (b - c)).
      private double sfMode
      Survival probability at the mode.
    • Constructor Summary

      Constructors 
      Modifier Constructor Description
      private TriangularDistribution​(double a, double c, double b)  
    • Field Detail

      • a

        private final double a
        Lower limit of this distribution (inclusive).
      • b

        private final double b
        Upper limit of this distribution (inclusive).
      • c

        private final double c
        Mode of this distribution.
      • divisor1

        private final double divisor1
        Cached value ((b - a) * (c - a).
      • divisor2

        private final double divisor2
        Cached value ((b - a) * (b - c)).
      • cdfMode

        private final double cdfMode
        Cumulative probability at the mode.
      • sfMode

        private final double sfMode
        Survival probability at the mode.
    • Constructor Detail

      • TriangularDistribution

        private TriangularDistribution​(double a,
                                       double c,
                                       double b)
        Parameters:
        a - Lower limit of this distribution (inclusive).
        c - Mode of this distribution.
        b - Upper limit of this distribution (inclusive).
    • Method Detail

      • of

        public static TriangularDistribution of​(double a,
                                                double c,
                                                double b)
        Creates a triangular distribution.
        Parameters:
        a - Lower limit of this distribution (inclusive).
        c - Mode of this distribution.
        b - Upper limit of this distribution (inclusive).
        Returns:
        the distribution
        Throws:
        java.lang.IllegalArgumentException - if a >= b, if c > b or if c < a.
      • getMode

        public double getMode()
        Gets the mode parameter of this distribution.
        Returns:
        the mode.
      • 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.
      • 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.

        For lower limit \( a \), upper limit \( b \), and mode \( c \), the mean is \( (a + b + c) / 3 \).

        Returns:
        the mean.
      • getVariance

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

        For lower limit \( a \), upper limit \( b \), and mode \( c \), the variance is \( (a^2 + b^2 + c^2 - ab - ac - bc) / 18 \).

        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 limit parameter a 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 limit parameter b of the distribution.

        Returns:
        the upper bound of the support.