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Maximum likelihood estimation for the generalized extreme value distribution

Source: R/mle.R
fit.gev.Rd

This function returns an object of class mev_gev, with default methods for printing and quantile-quantile plots. The default starting values are the solution of the probability weighted moments.

Usage

fit.gev(
  xdat,
  start = NULL,
  method = c("nlminb", "BFGS"),
  show = FALSE,
  fpar = NULL,
  warnSE = FALSE
)

Arguments

xdat

a numeric vector of data to be fitted.

start

named list of starting values

method

string indicating the outer optimization routine for the augmented Lagrangian. One of nlminb or BFGS.

show

logical; if TRUE (the default), print details of the fit.

fpar

a named list with optional fixed components loc, scale and shape

warnSE

logical; if TRUE, a warning is printed if the standard errors cannot be returned from the observed information matrix when the shape is less than -0.5.

Value

a list containing the following components:

  • estimate a vector containing the maximum likelihood estimates.

  • std.err a vector containing the standard errors.

  • vcov the variance covariance matrix, obtained as the numerical inverse of the observed information matrix.

  • method the method used to fit the parameter.

  • nllh the negative log-likelihood evaluated at the parameter estimate.

  • convergence components taken from the list returned by auglag. Values other than 0 indicate that the algorithm likely did not converge.

  • counts components taken from the list returned by auglag.

  • xdat vector of data

Examples

xdat <- mev::rgev(n = 100)
fit.gev(xdat, show = TRUE)
#> Log-likelihood: -152.4593 
#> 
#> Estimates
#>    loc   scale   shape  
#> -0.193   0.931   0.023  
#> 
#> Standard Errors
#>    loc   scale   shape  
#> 0.1091  0.0823  0.0954  
#> 
#> Optimization Information
#>   Convergence: successful 
#>   Function Evaluations: 51 
#>   Gradient Evaluations: 21 
#> 
# Example with fixed parameter
fit.gev(xdat, show = TRUE, fpar = list(shape = 0))
#> Log-likelihood: -152.4891 
#> 
#> Estimates
#>    loc   scale  
#> -0.182   0.939  
#> 
#> Standard Errors
#>    loc   scale  
#> 0.0989  0.0750  
#> 
#> Parameters
#>    loc   scale   shape  
#> -0.182   0.939   0.000  
#> 
#> Optimization Information
#>   Convergence: successful 
#>   Function Evaluations: 49 
#>   Gradient Evaluations: 16 
#>