R/quantMax.R
quantMaxFun.TVGEV.RdGiven an object with class "TVGEV" and a collection of time
blocks (or period) defined by date, the distribution
of the random maximum over the period \(M^\star := \max_b
Y_b\) is known. The corresponding quantile
function \(q_{M^\star}(m^\star)\) can be
obtained.
# S3 method for TVGEV
quantMaxFun(object, date = NULL, psi = NULL, theta = NULL, ...)An object with class "TVGEV".
An object that can be coerced to the class
"Date". If not provided this will be taken as the date
attached to object.
An optional vector of coefficients for
object. By default the ML estimate as returned by
coef(object) is used.
An optional matrix with three columns containing GEV
parameters. The colums are in the order location,
scale and shape. When this argument is used
neither date not psi can be used.
Not used.
A function (more precisely, a closure). This function has
a single formal argument p representing a probability
\(p\), and it returns the corresponding quantile \(q\)
such that
\(\text{Pr}\{M^\star \leq q \} = p\) where
\(M^\star\) is the random maximum.
This function computes the quantile by using the distribution
function \(F_{M^\star}\) returned by
cdfMaxFun.TVGEV and the uniroot
function to solve the equation \(F_{M^\star}(q) = p\). By contrast quantMax.TVGEV computes the values of the
distribution values \(p_i\) corresponding to a grid of quantiles
\(q_i\) and interpolates to find the quantiles corresponding to
the probability values provided by the user. So small differences
will exist in the results.
When theta is given model is not
used. The quantile function is simply that of the maximum of
independent r.vs following GEV distributions with their
parameters given by (the rows of) theta.
cdfMaxFun.TVGEV for the corresponding
quantile function (or closure).
df <- within(TXMax_Dijon, Date <- as.Date(sprintf("%4d-01-01", Year)))
## fit a TVGEV model. Only the location parameter is TV.
res1 <- TVGEV(data = df, response = "TXMax", date = "Date",
design = breaksX(date = Date, breaks = "1970-01-01", degree = 1),
loc = ~ t1 + t1_1970)
qf <- quantMaxFun(res1)
qf(c(0.90, 0.99, 0.999))
#> [1] 40.21668 41.38380 42.22238
## a 'new period'
date <- as.Date(sprintf("%4d-01-01", 2025:2054))
qfNew <- quantMaxFun(res1, date = date)
qfNew(c(0.90, 0.99, 0.999))
#> [1] 42.11925 43.39069 44.24913