Class ReturnLevel

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

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, \[ \begin{eqnarray} P(X > \eta) invalid input: '&' = invalid input: '&' \frac{1}{T} \\ 1 - F_X(\eta) invalid input: '&' = invalid input: '&' \frac{1}{T} \\ F_X(\eta) invalid input: '&' = invalid input: '&' 1 - \frac{1}{T} \\ \eta invalid input: '&' = invalid input: '&' F^{-1}(1 - \frac{1}{T}) \end{eqnarray} \] where \(F^{-1}\) is the inverse of the CDF, or quantile function of the distribution.
  • Constructor Details

    • ReturnLevel

      public ReturnLevel(UnivariateEVD evd)
      Construct the return level function for a given univariate extreme value distribution.
      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.
      cdfInverse - the inverse of the cdf
  • Method Details

    • evaluate

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