R/NSGEV.R
rho2psi.RdFind the complete vector of NSGEV parameters from a partial vector and a Return Level.
rho2psi(rho, nm1, psi_m1, model, data = NULL, type = "expect")A fixed Return Level (RL).
Name of the parameter which is adjusted.
Vector of NSGEV parameters with its element
nm1 removed.
The NSGEV model.
Data frame of covariates.
The type of Return Level.
A vector \(\boldsymbol{\psi}\) of NSGEV parameters.
In a Non-Sationary framework, a Return Level (RL) rho
relates to a given value of the covariates or to a distribution of
the covariates. This distribution is assumed here to be given by
the observations in data, assuming that the corresponding
Return Period is equal to the number of observations understood as
a multiple of the block duration. When type = "expect" the
RL is the value \(\rho\) for which the random number of
exceedances over \(\rho\) has unit expectation.
This function is a technical function to profile the likelihood. One of the NSGEV model parameter, say \(\psi_1\), is adjusted to reach the given value RL, the other elements of \(\psi\) being given and fixed. These later elements form a vector \(\boldsymbol{\psi}_{-1}\) with length \(p-1\), where \(p\) is the number of model parameters. Now for a given value of \(rho\), the value of the profile log-likelihood \(\ell(\rho)\) is obtained by maximising the log-likelihood w.r.t \(\boldsymbol{\psi}_{-1}\).
df <- data.frame(t = 1:10)
fit <- NSGEV(formulas = list("loc" = ~ alpha + beta * t, "scale" = ~ delta, "shape" = ~ xi),
data = df)
df.new <- data.frame(t = 11:20)
psi <- c("alpha" = 1, "beta" = 0.01, "delta" = 0.6, "xi" = 0.06)
rho2psi(rho = 30, nm1 = "alpha", psi_m1 = psi[-1], model = fit, data = df.new)
#> alpha beta delta xi
#> 28.39881 0.01000 0.60000 0.06000
rho2psi(rho = 40, nm1 = "alpha", psi_m1 = psi[-1], model = fit, data = df.new)
#> alpha beta delta xi
#> 38.39881 0.01000 0.60000 0.06000