Package org.hipparchus.distribution.continuous

Class TriangularDistribution

    • Constructor Detail

      • TriangularDistribution

        public TriangularDistribution​(double a,
                              double c,
                              double b)
                       throws MathIllegalArgumentException
        Creates a triangular real distribution using the given lower limit, upper limit, and mode.
        Parameters:
        a - Lower limit of this distribution (inclusive).
        b - Upper limit of this distribution (inclusive).
        c - Mode of this distribution.
        Throws:
        MathIllegalArgumentException - if a >= b or if c > b.
        MathIllegalArgumentException - if c < a.

    • Method Detail

      • getMode

        public double getMode()
        Returns the mode c of this distribution.
        Returns:
        the mode c of this 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 - the point at which the PDF is evaluated
        Returns:
        the value of the probability density function at point 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 - the 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

      • getNumericalMean

        public double getNumericalMean()
        Use this method to get the numerical value of 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

      • getNumericalVariance

        public double getNumericalVariance()
        Use this method to get the numerical value of 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 (possibly Double.POSITIVE_INFINITY as for certain cases in TDistribution) or Double.NaN if it is not defined

      • getSupportLowerBound

        public double getSupportLowerBound()
        Access the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0). In other words, this method must return

        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()
        Access the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1). In other words, this method must return

        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()
        Use this method to get information about 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