# Class ReturnLevel

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

public class ReturnLevel
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.

## Nested classes/interfaces inherited from interface dev.nm.analysis.function.Function

Function.EvaluationException
• ## Constructor Summary

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

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

### Methods inherited from class dev.nm.analysis.function.rn2r1.univariate.AbstractUnivariateRealFunction

evaluate

### Methods inherited from class dev.nm.analysis.function.rn2r1.AbstractRealScalarFunction

dimensionOfDomain, dimensionOfRange

### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

### Methods inherited from interface dev.nm.analysis.function.Function

dimensionOfDomain, dimensionOfRange
• ## 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