Package org.apache.commons.statistics.distribution

Class TriangularDistribution

    • Constructor Detail

      • TriangularDistribution

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

    • Method Detail

      • getMode

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

      • 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. For lower limit a, upper limit b and mode c, the PDF is given by
        • 2 * (x - a) / [(b - a) * (c - a)] if a <= x < c,
        • 2 / (b - a) if x = c,
        • 2 * (b - x) / [(b - a) * (b - c)] if c < x <= b,
        • 0 otherwise.
        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. For lower limit a, upper limit b and mode c, the CDF is given by
        • 0 if x < a,
        • (x - a)^2 / [(b - a) * (c - a)] if a <= x < c,
        • (c - a) / (b - a) if x = c,
        • 1 - (b - x)^2 / [(b - a) * (b - c)] if c < x <= b,
        • 1 if x > b.
        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.

      • 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, or Double.NaN if it is not defined.

      • 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 - a * b - a * c - b * c) / 18.
        Returns:
        the variance, or Double.NaN if it is not defined.

      • 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 R | P(X <= x) > 0}. The lower bound of the support is equal to the lower limit parameter a of the distribution.
        Returns:
        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 R | P(X <= x) = 1}. The upper bound of the support is equal to the upper limit parameter b of the distribution.
        Returns:
        upper bound of the support

      • isSupportConnected

        public boolean isSupportConnected()
        Indicates whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support. The support of this distribution is connected.
        Returns:
        true

      • sample

        public static double[] sample​(int n,
                              ContinuousDistribution.Sampler sampler)
        Utility function for allocating an array and filling it with n samples generated by the given sampler.
        Parameters:
        n - Number of samples.
        sampler - Sampler.
        Returns:
        an array of size n.