Class TriangularDistribution

Method Details

• getMode

  public double getMode()

  Returns the mode c of this distribution.

  Returns:

  the mode c of this distribution

• getSolverAbsoluteAccuracy

  protected double getSolverAbsoluteAccuracy()

  Returns the solver absolute accuracy for inverse cumulative computation. You can override this method in order to use a Brent solver with an absolute accuracy different from the default.

  For this distribution, the returned value is not really meaningful, since exact formulas are implemented for the computation of the inverseCumulativeProbability(double) (no solver is invoked).

  For lower limit a and upper limit b, the current implementation returns max(ulp(a), ulp(b).

  Overrides:

  getSolverAbsoluteAccuracy in class AbstractRealDistribution

  Returns:

  the maximum absolute error in inverse cumulative probability estimates

• 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 invalid input: '<'= 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 invalid input: '<'= 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

• isSupportLowerBoundInclusive

  public boolean isSupportLowerBoundInclusive()

  Whether or not the lower bound of support is in the domain of the density function. Returns true iff getSupporLowerBound() is finite and density(getSupportLowerBound()) returns a non-NaN, non-infinite value.

  Returns:

  true if the lower bound of support is finite and the density function returns a non-NaN, non-infinite value there

• isSupportUpperBoundInclusive

  public boolean isSupportUpperBoundInclusive()

  Whether or not the upper bound of support is in the domain of the density function. Returns true iff getSupportUpperBound() is finite and density(getSupportUpperBound()) returns a non-NaN, non-infinite value.

  Returns:

  true if the upper bound of support is finite and the density function returns a non-NaN, non-infinite value there

• 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 OutOfRangeException

  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(Xinvalid input: '<'=x) >= p} for 0 < p <= 1,
  • inf{x in R | P(Xinvalid input: '<'=x) > 0} for p = 0.

  The default implementation returns

  • RealDistribution.getSupportLowerBound() for p = 0,
  • RealDistribution.getSupportUpperBound() for p = 1.

  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:

  OutOfRangeException - if p < 0 or p > 1