Distribution Function for the Random Maximum on a given Period

Given 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 distribution function can be obtained.

# S3 method for TVGEV
cdfMaxFun(object, date = NULL, psi = NULL, theta = NULL, ...)

Arguments

object

An object with class "TVGEV".

date

An object that can be coerced to the class "Date". If not provided this will be taken as the date attached to object.

psi

An optional vector of coefficients for object. By default the ML estimate as returned by coef(object) is used.

theta

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.

Value

A function (more precisely, a closure). This function has a single formal argument q representing a quantile, and it returns the corresponding probability

\(\text{Pr}\{M^\star \leq q \}\).

Caution

When theta is given model is not used. The distribution function is simply that of the maximum of independent r.vs following GEV distributions with their parameters given by (the rows of) theta.

See also

quantMaxFun.TVGEV for the corresponding quantile function (or closure).

Examples

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)
cdf <- cdfMaxFun(res1)
cdf(c(39.0, 41.0))
#> [1] 0.5190225 0.9766100

## a 'new period'
date <- as.Date(sprintf("%4d-01-01", 2025:2054))
cdfNew <- cdfMaxFun(res1, date = date)
cdfNew(c(39.0, 41.0))
#> [1] 0.03275412 0.62318687