fit.ghypuv {ghyp}R Documentation

Fitting generalized hyperbolic distributions to univariate data

Description

This function performs a maximum likelihood parameter estimation for univariate generalized hyperbolic distributions.

Usage

fit.ghypuv(data, lambda = 1, alpha.bar = 0.1, mu = mean(data), 
           sigma = sd(data), gamma = 0, 
           opt.pars = c(lambda = T, alpha.bar = T, mu = T, 
                        sigma = T, gamma = !symmetric), 
           symmetric = F, standardize = F, save.data = T, 
           na.rm = T, silent = FALSE, ...)
           
fit.hypuv(data, 
          opt.pars = c(alpha.bar = T, mu = T, sigma = T, gamma = !symmetric), 
          symmetric = F, ...)

fit.NIGuv(data, 
          opt.pars = c(alpha.bar = T, mu = T, sigma = T, gamma = !symmetric), 
          symmetric = F, ...)

fit.VGuv(data, lambda = 1, 
         opt.pars = c(lambda = T, mu = T, sigma = T, gamma = !symmetric), 
         symmetric = F, ...)

fit.tuv(data, nu = 3.5, 
        opt.pars = c(nu = T, mu = T, sigma = T, gamma = !symmetric), 
        symmetric = F, ...)

Arguments

data An object coercible to a vector.
lambda Shape parameter.
alpha.bar Shape parameter.
nu Shape parameter only used in case of a student-t distribution. It determines the degree of freedom and is defined as -2*lambda.
mu Location parameter.
sigma Dispersion parameter.
gamma Skewness parameter.
opt.pars A named logical vector which states which parameters should be fitted.
symmetric If TRUE the skewness parameter gamma keeps zero.
standardize If TRUE the sample will be standardized before fitting. Afterwards, the parameters and log-likelihood et cetera will be back-transformed.
save.data If TRUE data will be stored within the mle.ghyp object.
na.rm If TRUE missing values will be removed from data.
silent If TRUE no prompts will appear in the console.
... Arguments passed to optim and to fit.ghypuv when fitting special cases of the generalized hyperbolic distribution.

Details

The general-purpose optimization routine optim is used to maximize the loglikelihood function. The default method is that of Nelder and Mead which uses only function values. Parameters of optim can be passed via the ... argument of the fitting routines.

Value

An object of class mle.ghyp.

Note

The variance gamma distribution becomes singular when x - m = 0. This singularity is catched and the reduced density function is computed. Because the transition is not smooth in the numerical implementation this can rarely result in nonsensical fits.

Providing both arguments, opt.pars and symmetric respectively, can result in a conflict when opt.pars['gamma'] and symmetric are TRUE. In this case symmetric will dominate and opt.pars['gamma'] is set to FALSE.

Author(s)

Wolfgang Breymann, David Lüthi

See Also

fit.ghypmv, fit.hypmv, fit.NIGmv, fit.VGmv, fit.tmv for multivariate fitting routines.

Examples

  data(smi.stocks)
  fit.NIGuv(data = smi.stocks[,"SMI"], opt.pars = c(alpha.bar = FALSE),
            alpha.bar = 1, control = list(abs.tol = 1e-5, maxit = 100))

[Package ghyp version 1.0.0 Index]