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, \[ \begin{eqnarray} P(X > \eta) & = & \frac{1}{T} \\ 1 - F_X(\eta) & = & \frac{1}{T} \\ F_X(\eta) & = & 1 - \frac{1}{T} \\ \eta & = & F^{-1}(1 - \frac{1}{T}) \end{eqnarray} \] where \(F^{-1}\) is the inverse of the CDF, or quantile function of the distribution.

Nested Class Summary

Nested classes/interfaces inherited from interface dev.nm.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

Modifier and Type	Method and 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 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