Package org.hipparchus.distribution.continuous

Class TriangularDistribution

java.lang.Object
org.hipparchus.distribution.continuous.AbstractRealDistribution
org.hipparchus.distribution.continuous.TriangularDistribution
All Implemented Interfaces:
Serializable, RealDistribution
public class TriangularDistribution extends AbstractRealDistribution
Implementation of the triangular real distribution.
See Also:

  • Constructor Details

    • 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 Details

    • 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

    • inverseCumulativeProbability

      public double inverseCumulativeProbability(double p) throws MathIllegalArgumentException
      Computes the quantile function of this distribution. For a random variable X distributed according to this distribution, the returned value is
      • inf{x in R | P(X<=x) >= p} for 0 < p <= 1,
      • inf{x in R | P(X<=x) > 0} for p = 0.
      The default implementation returns
      Specified by:
      inverseCumulativeProbability in interface RealDistribution
      Overrides:
      inverseCumulativeProbability in class AbstractRealDistribution
      Parameters:
      p - the cumulative probability
      Returns:
      the smallest p-quantile of this distribution (largest 0-quantile for p = 0)
      Throws:
      MathIllegalArgumentException - if p < 0 or p > 1