return.level: The associated return level

In hkevp: Spatial Extreme Value Analysis with the Hierarchical Model of Reich and Shaby (2012)

The associated return level

Description

Computation of the associated return level with given period and GEV parameters.

Usage

return.level(period, 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.

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] ~.

Value

A numerical value or a numerical vector, depending on the input arguments loc, scale, shape

Author(s)

Quentin Sebille

Examples

return.level(period = 100, loc = 1, scale = 1, shape = 1)
return.level(period = 200, loc = 1:10, scale = 1, shape = 0)

hkevp documentation built on April 18, 2023, 5:11 p.m.