bvmle: Maximum-likelihood Fitting of Bivariate Extreme Value Distributions

Description

Maximum-likelihood estimates for the logistic (symmetric and asymmetric), negative logistic (symmetric and asymmetric) and Husler-Reiss models, allowing any of the parameters (including marginal parameters) to be held fixed if desired.

Usage

fbvlog(x, start, ...)
fbvalog(x, start, ...)
fbvhr(x, start, ...)
fbvneglog(x, start, ...)
fbvaneglog(x, start, ...)

Arguments

a matrix or data frame with two columns.

start

a named list giving the parameters to be optimized with initial values (see Details).

...

additional parameters, either for the distribution or for optim. If parameters of the distribution are included they will be held fixed (see Details). If parameters of the distribution are not included either here or as

Value

A list with with components
estimatea vector containing the maximum likelihood estimates.
std.erra vector containing the standard errors.
deviancethe deviance at the maximum likelihood estimates.
countsa two-element integer vector giving the number of calls to the log-likelihood function and the number gradient approximations respectively.

Details

Maximization of the log-likelihood is performed. The estimated standard errors are taken from the observed information, calculated by a numerical approximation.

The named components of start can be any or possibly all of dep, asy (a vector of length two), mar1 and mar2 (vectors of length three). Alternatively, mar1 can be passed as three separate arguments; loc1, scale1 and shape1. mar2 can be similarly passed as three separate arguments; loc2, scale2 and shape2. The asymmetry parameters can also be passed separately as asy1 and asy2. Associating a separate name with each parameter allows any parameter subset to be fixed at specified values. All parameters to be fixed must be passed individually (e.g. to fix the parameters on the first margin all of loc1, scale1 and shape1 must be specified; using mar1 to specify all three simultaneously results in an error).

Examples

Run this code

bvdata <- rbvlog(100, dep = 0.6, mar1 = c(1.2,1.4,0.4),
mar2 = c(1.2,1.4,0.4))
fbvlog(bvdata, start = list(mar1 = c(2,1,0), mar2 = c(1,1,0), dep = 0.75), 
method="BFGS")
fbvlog(bvdata, start = list(mar1 = c(2,1,0), mar2 = c(1,1,0)), dep = 1, 
method="BFGS")
fgev(bvdata[,1], start = list(loc=1,scale=1,shape=0),
method="BFGS")$estimate
fgev(bvdata[,2], start = list(loc=1,scale=1,shape=0),
method="BFGS")$estimate