fit.ghypuv: Fitting generalized hyperbolic distributions to univariate...
In ghyp: Generalized Hyperbolic Distribution and Its Special Cases

fit.ghypuv

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 = 0.5, mu = median(data),
           sigma = mad(data), gamma = 0,
           opt.pars = c(lambda = TRUE, alpha.bar = TRUE, mu = TRUE,
                        sigma = TRUE, gamma = !symmetric),
           symmetric = FALSE, standardize = FALSE, save.data = TRUE,
           na.rm = TRUE, silent = FALSE, ...)

fit.hypuv(data,
          opt.pars = c(alpha.bar = TRUE, mu = TRUE, sigma = TRUE, gamma = !symmetric),
          symmetric = FALSE, ...)

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

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

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

fit.gaussuv(data, na.rm = TRUE, save.data = TRUE)

Arguments

`data`	An object coercible to a `vector`.
`lambda`	Starting value for the shape parameter `lambda`.
`alpha.bar`	Starting value for the shape parameter `alpha.bar`.
`nu`	Starting value for the shape parameter `nu` (only used in case of a student-t distribution. It determines the degree of freedom and is defined as `-2*lambda`.)
`mu`	Starting value for the location parameter `mu`.
`sigma`	Starting value for the dispersion parameter `sigma`.
`gamma`	Starting value for the skewness parameter `gamma`.
`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 - \mu = 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 Luethi

References

ghyp-package vignette in the doc folder or on https://cran.r-project.org/package=ghyp.

Examples

  data(smi.stocks)

  nig.fit <- fit.NIGuv(smi.stocks[,"SMI"], opt.pars = c(alpha.bar = FALSE),
                       alpha.bar = 1, control = list(abstol = 1e-8))
  nig.fit

  summary(nig.fit)

  hist(nig.fit)

ghyp documentation built on Aug. 21, 2023, 5:12 p.m.