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Generalized Log-Likelihood Functions for GEV Models

Source: R/utils-generalized-likelihood.R
utils_generalized_likelihood.Rd

Computes the generalized log-likelihood for stationary and nonstationary variants of the Generalized Extreme Value (GEV) distribution with a geophysical (Beta) prior distribution for the shape parameter (Martins and Stedinger, 2000).

For NS-FFA: To compute the generalized log-likelihood for a nonstationary probability model, include the observation years (ns_years) and the nonstationary model structure (ns_structure).

Usage

utils_generalized_likelihood(
  data,
  params,
  prior,
  ns_years = NULL,
  ns_structure = NULL
)

Arguments

data

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

params

Numeric vector of distribution parameters, in the order (location, scale, shape). The length must be between 2 and 5, depending on the specified distribution and structure.

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.

Value

Numeric scalar. The generalized log-likelihood value.

Details

The generalized log-likelihood is defined as sum of (1) the log-likelihood and (2) the log-density of the Beta prior with parameters \((p, q)\). The contribution of the prior is: $$\log \pi(\kappa) = (p-1) \log(0.5-\kappa) + (q-1) \log(0.5+\kappa) - \log (\beta(p, q))$$

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. 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. doi:10.1029/1999WR900330

See also

utils_log_likelihood()

Examples

data <- rnorm(n = 100, mean = 100, sd = 10)
params <- c(100, 10, 0.1)
prior <- c(1, 1)

# Compute the generalized log-likelihood
utils_generalized_likelihood(data, params, prior)
#> [1] -411.0723