Class ReturnLevel

  • All Implemented Interfaces:
    Function<Vector,​Double>, RealScalarFunction, UnivariateRealFunction
    Direct Known Subclasses:
    ACERReturnLevel

    public class ReturnLevel
    extends AbstractUnivariateRealFunction
    Given a GEV distribution of a random variable \(X\), the return level \(\eta\) is the value that is expected to be exceeded on average once every interval of time \(T\), with a probability of \(1 / T\). Therefore, \[ \begin{eqnarray} P(X > \eta) & = & \frac{1}{T} \\ 1 - F_X(\eta) & = & \frac{1}{T} \\ F_X(\eta) & = & 1 - \frac{1}{T} \\ \eta & = & F^{-1}(1 - \frac{1}{T}) \end{eqnarray} \] where \(F^{-1}\) is the inverse of the CDF, or quantile function of the distribution.
    • Constructor Detail

      • ReturnLevel

        public ReturnLevel​(UnivariateEVD evd)
        Construct the return level function for a given univariate extreme value distribution.
        Parameters:
        evd - the univariate extreme value distribution
      • ReturnLevel

        public ReturnLevel​(UnivariateRealFunction cdfInverse)
        Construct the return level function with the inverse function of a univariate extreme value distribution. This is suitable when only the cdf is known.
        Parameters:
        cdfInverse - the inverse of the cdf
    • Method Detail

      • evaluate

        public double evaluate​(double returnPeriod)
        Compute the return level from the given return period.
        Parameters:
        returnPeriod - the length of the return period
        Returns:
        the return level