Computation of the associated return level with given period and GEV parameters.
Usage
return.level(period, loc, scale, shape)
Value
A numerical value or a numerical vector, depending on the input arguments loc, scale, shape
Arguments
period
An integer indicating the wished return period T.
loc
A numerical value or vector for the GEV location parameter. Must be of length one or same length as scale and/or shape.
scale
A numerical value or vector for the GEV scale parameter. Must be of length one or same length as loc and/or shape.
shape
A numerical value or vector for the GEV shape parameter. Must be of length one or same length as loc and/or scale.
Author
Quentin Sebille
Details
The \(T\)-year return level is a common value of risk in Extreme Value Theory. It represents the value that is expected to be exceeded once over \(T\) years by the annual maxima. Given the parameters \(\mu\), \(\sigma\) and \(\xi\) of the GEV distribution associated to the yearly maxima, we can compute the associated \(T\)-return level \(y_T\) by:
$$y_T := \mu + \frac{\sigma}{\xi} \left[ \log\left(\frac{T}{T-1}\right)^{-\xi} -1 \right] ~.$$