bgev (version 0.2)

bgev.mle: Parameter estimation of bimodal GEV distribution based on real data that appears to be bimodal.

Description

Finds the maximum likelihood estimators of the bimodal GEV distribution parameters by minimizing the log-likelihood function of the data.

The estimation procedure is a divided into three steps:

1) Use egevd for starting values: We estimate the data using a unimodal GEV distribution (function egevd from package EnvStats). This is justified by the fact that the bgev distribution with delta = 0 is a unimodal GEV distribution with parametesr mu sigma and xi.

2) DEOptim for more adequate starting values: Use the starting values to create lower and upper bounds and feed it into DEOptim to get starting values for all parameters simutaneously.

3) Use optim for local search with starting values for DEOptim.

Usage

bgev.mle(x, method_envstats = "mle", deoptim.itermax = 200, 
optim.method = "L-BFGS-B",start = NULL, lower = NULL, upper = NULL)

Value

A list with components returned by the optim R function for which the main values are

par

best parameters of bimodal gev fitting the data

value

value of the log-likelihood corresponding to 'par'

Arguments

x

a unidimensional vector containing observations to estimate a bimodal GEV distribution

start

a vector of dimension 4 containing the starting values for each of the bimodal GEV parameters where the search is going to take place.

lower

a vector of dimension 4 containing the lower limit for each of the bimodal GEV parameters where the search is going to take place.

upper

a vector of dimension 4 containing the upper limit for each of the bimodal GEV parameters where the search is going to take place.

method_envstats

method to use in the egevd function from envstats package.

deoptim.itermax

number of iterations in the deoptim step.

optim.method

maximum number of interations when finding a good starting value for the optimization algorithm.

Author

tools:::Rd_package_author("bgev")

References

OTINIANO, Cira EG, et al. (2023). A bimodal model for extremes data. Environmental and Ecological Statistics, 1-28. http://dx.doi.org/10.1007/s10651-023-00566-7

Examples

# generate 100 values distributed according to a bimodal GEV
x = rbgev(50, mu = 0.2, sigma = 1, xi = 0.5, delta = 0.2) 
# estimate the bimodal GEV parameters using the generated data
bgev.mle(x)