Class TriangularDistribution

java.lang.Object
org.apache.commons.statistics.distribution.AbstractContinuousDistribution
org.apache.commons.statistics.distribution.TriangularDistribution
All Implemented Interfaces:
ContinuousDistribution
public final class TriangularDistribution extends AbstractContinuousDistribution
Implementation of the triangular distribution.

The probability density function of \( X \) is:

\[ f(x; a, b, c) = \begin{cases} \frac{2(x-a)}{(b-a)(c-a)} & \text{for } a \le x \lt c \\ \frac{2}{b-a} & \text{for } x = c \\ \frac{2(b-x)}{(b-a)(b-c)} & \text{for } c \lt x \le b \\ \end{cases} \]

for \( -\infty \lt a \le c \le b \lt \infty \) and \( x \in [a, b] \).

See Also:

  • Field Details

    • 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 Details

    • 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 Details

    • 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:
      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.

    • 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)
      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.