Return level and expected shortfall for the EVBS regression model

Computes the period-observation return level and, optionally, the conditional tail expectation (expected shortfall) at a given linear predictor value.

Usage

evbs_return_level(object, x, period, es = FALSE)

Arguments

object: An object of class evbsreg from evbsreg.fit.
x: Covariate vector (including the intercept) at which to evaluate.
period: Return period, expressed in the units of one observation. For monthly maxima and a \(T\)-year return level, use period = 12 * T.
es: Logical; if TRUE, also return the expected shortfall.

Value

A named numeric vector with the return level and, if requested, the expected shortfall.

Details

The return level is the quantile of order \(1 - 1/\code{period}\) of the fitted conditional distribution of one observation at covariate value x: it is exceeded on average once in period observations with that covariate value, not a return level of the marginal distribution. With monthly maxima, period = 12 * T gives the level exceeded once in \(12T\) months; reading it as the \(T\)-year level of the annual maximum assumes the monthly maxima of a year are independent. Periods much longer than the record are extrapolations.

Examples

data(itajai)
fit <- evbsreg.fit(cbind(1, itajai$pressure), itajai$wind)
# 50-year return level at mean pressure, from monthly maxima
evbs_return_level(fit, x = c(1, mean(itajai$pressure)),
                  period = 12 * 50, es = TRUE)
#>       return_level expected_shortfall 
#>           27.60566           29.20929