ffaframework (version 0.1.0)

fit_gmle: Generalized Maximum Likelihood Parameter Estimation

Description

Estimates the parameters of the generalized extreme value (GEV) distribution by maximizing the generalized log‐likelihood, which incorporates a Beta prior on the shape parameter. Initial parameter estimates are obtained using the method of L‐moments and optimization is performed via stats::nlminb() with repeated perturbations if needed.

For NS-FFA: To estimate parameters for a nonstationary model, include the observation years (ns_years) and the nonstationary model structure (ns_structure).

Usage

fit_gmle(data, prior, ns_years = NULL, ns_structure = NULL)

Value

A list containing the results of parameter estimation:

• data: The data argument.

• prior: The prior argument.

• ns_years: The ns_years argument, if given.

• ns_structure: The ns_structure argument, if given.

• method: "GMLE".

• params: Numeric vector of estimated parameters.

• mll: The maximum value of the generalized log‐likelihood.

Arguments

data

Numeric vector of observed annual maximum series values. Must be strictly positive, finite, and not missing.

prior

Numeric vector of length 2. Specifies the parameters of the Beta prior for the shape parameter \(\kappa\).

ns_years

For NS-FFA only: Numeric vector of observation years corresponding to data. Must be the same length as data and strictly increasing.

ns_structure

For NS-FFA only: Named list indicating which distribution parameters are modeled as nonstationary. Must contain two logical scalars:

• location: If TRUE, the location parameter has a linear temporal trend.

• scale: If TRUE, the scale parameter has a linear temporal trend.

Details

1. Calls fit_lmoments() on the data to obtain initial parameter estimates.

2. Initializes trend parameters to zero if necessary.

3. Defines an objective function using utils_generalized_likelihood().

4. Runs stats::nlminb() with box constraints. Attempts minimization up to 100 times.

References

El Adlouni, S., Ouarda, T.B.M.J., Zhang, X., Roy, R., Bobee, B., 2007. Generalized maximum likelihood estimators for the nonstationary generalized extreme value model. Water Resources Research 43 (3), 1–13. tools:::Rd_expr_doi("10.1029/2005WR004545")

Martins, E. S., and Stedinger, J. R. (2000). Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data. Water Resources Research, 36(3), 737–744. tools:::Rd_expr_doi("10.1029/1999WR900330")

See Also

utils_generalized_likelihood(), fit_lmoments(), stats::nlminb()

Examples

data <- rnorm(n = 100, mean = 100, sd = 10)
prior <- c(6, 9)
ns_years <- seq(from = 1901, to = 2000)
ns_structure <- list(location = TRUE, scale = FALSE)
fit_gmle(data, prior, ns_years, ns_structure)