Compute an Estimate of the Tail Coefficient 'xi' using Quantile Regression Results
xi.rqTList.RdEstimate the tail coefficient \(\xi\) from quantiles.
Usage
# S3 method for rqTList
xi(object, tau = NULL, lastFullYear = TRUE, plot = FALSE, ...)Arguments
- object
An object with class
"rqTList".- tau
A vector of 3 probabilities. This vector must be in strictly increasing order and contain values that are found in
tau(object). By default the three largest values intau(object)are used.- lastFullYear
Logical. It
TRUEthe value of the estimatedxiis computed for the last full year of the data used to createdata. Seepredict.rqTList.- plot
Logical. If
TRUEa (gg)plot is shown.- ...
Not used yet.
Details
Let \(\tau_1 < \tau_2 < \tau_3\) be the probabilities and \(T_1 < T_2 < T_3\) be the corresponding return periods \(T_i = 1 / (1 - \tau_i)\). Let \(q_1\), \(q_2\), \(q_3\) be the corresponding quantiles as computed by quantile regression. Then we can find \(\xi\) by solving the equation $$\frac{T_3^\xi - T_1^\xi}{T_2^\xi - T_1^\xi} = \frac{q_3 - q_1}{q_2 - q_1}.$$ The value of \(\xi\) then depends on the covariates used in the quantile regression. We only consider here the case where the quantiles depend on the date, with emphasis on the case where the quantile are periodic functions of the date with one-year period. The the value of \(\xi\) has also the one-year periodicity, and we can assess its variation on a one-year period which can be the last full year in the period used to estimate the quantiles.