Package dev.nm.stat.evt.function

Class ReturnLevel

java.lang.Object
dev.nm.analysis.function.rn2r1.AbstractRealScalarFunction
dev.nm.analysis.function.rn2r1.univariate.AbstractUnivariateRealFunction
dev.nm.stat.evt.function.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, \[ \begin{eqnarray} P(X > \eta) invalid input: '&' = invalid input: '&' \frac{1}{T} \\ 1 - F_X(\eta) invalid input: '&' = invalid input: '&' \frac{1}{T} \\ F_X(\eta) invalid input: '&' = invalid input: '&' 1 - \frac{1}{T} \\ \eta invalid input: '&' = invalid input: '&' F^{-1}(1 - \frac{1}{T}) \end{eqnarray} \] 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.
      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 Details

    • 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