glme.gev: Generalized L-moments estimation for generalized extreme value distribution

Description

This function estimates the Generalized L-moments of Generalized Extreme Value distribution.

Usage

glme.gev(
  xdat,
  ntry = 10,
  pen = "beta",
  pen.choice = NULL,
  mu = -0.5,
  std = 0.2,
  p = 6,
  c1 = 10,
  c2 = 5
)

Value

The glme.gev function returns a list containing the following elements:

para.glme - The estimated parameters of the Generalized Extreme Value distribution.
para.lme - The L-moment estimates of the parameters.
covinv.lmom - The inverse of the covariance matrix of the L-moments.
lcovdet - The log determinant of the covariance matrix.
nllh.glme - The negative log-likelihood of the GLME solution.
pen - The penalization method used.
p_q - (for beta penalty) The p and q values used.
c1_c2 - (for beta penalty) The c1 and c2 values used.
mu_std - (for norm penalty) The mu and std values used.

Arguments

xdat: A numeric vector of data to be fitted.
ntry: Number of attempts for parameter estimation. Higher values increase the chance of finding a more accurate estimate by trying different initial conditions.
pen: Type of penalty function: Choose among "norm", "beta" (default), "ms", "park", "cannon", "cd", and "no" (without penalty function).
pen.choice: Choice number of penalty function specifying hyperparameters. For "beta": 1-6 correspond to different (p, c1, c2) combinations. For "norm": 1-4 correspond to different (mu, std) combinations.
mu: Mean hyperparameter for "norm" penalty function (default -0.5).
std: Standard deviation hyperparameter for "norm" penalty function (default 0.2).
p: Shape hyperparameter for "beta" penalty function (default 6).
c1: Scaling hyperparameter for "beta" penalty function (default 10).
c2: Upper limit hyperparameter for "beta" penalty function (default 5).

Author

Yonggwan Shin, Seokkap Ko, Jihong Park, Yire Shin, Jeong-Soo Park

Details

The equations for the L-moments for LME of the GEVD are $$ \underline{\bf \lambda} - \underline{\bf l} = \underline{\bf 0},$$ where $ \underline{\bf \lambda} =(\lambda_1,\; \lambda_2,\; \lambda_3)^t $ and $\underline{\bf l} =(l_1,\; l_2,\; l_3)^t$. Next, we define the generalized L-moments distance (GLD) as; $$(\underline{\bf \lambda} -\underline{\bf l})^t V^{-1} (\underline{\bf \lambda} -\underline{\bf l}),$$ where $V$ is the variance-covariance matrix of the sample L-moments up to the third order.

References

Shin, Y., Shin, Y., Park, J. & Park, J.-S. (2025). Generalized method of L-moment estimation for stationary and nonstationary extreme value models. arXiv preprint arXiv:2512.20385. tools:::Rd_expr_doi("10.48550/arXiv.2512.20385")

Examples

Run this code

# Load example streamflow data
data(streamflow)
x <- streamflow$r1

# Estimate GEV parameters using beta penalty (default)
result <- glme.gev(x, ntry = 5)
print(result$para.glme)

# Using Martins-Stedinger penalty
result_ms <- glme.gev(x, ntry = 5, pen = "ms")
print(result_ms$para.glme)

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