# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.stats.evt.function

## 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.

• ### Nested classes/interfaces inherited from interface com.numericalmethod.suanshu.analysis.function.Function

Function.EvaluationException
• ### Constructor Summary

Constructors
Constructor and Description
ReturnLevel(UnivariateEVD evd)
Construct the return level function for a given univariate extreme value distribution.
ReturnLevel(UnivariateRealFunction cdfInverse)
Construct the return level function with the inverse function of a univariate extreme value distribution.
• ### Method Summary

All Methods
Modifier and Type Method and Description
double evaluate(double returnPeriod)
Compute the return level from the given return period.

evaluate
• ### 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