fBasics (version 3011.87)

ghtFit: GHT Distribution Fit

Description

Estimates the distributional parameters for a generalized hyperbolic Student-t distribution.

Usage

ghtFit(x, beta = 0.1, delta = 1, mu = 0, nu = 10, scale = TRUE, doplot = TRUE, span = "auto", trace = TRUE, title = NULL, description = NULL, ...)

Arguments

beta, delta, mu
numeric values. beta is the skewness parameter in the range (0, alpha); delta is the scale parameter, must be zero or positive; mu is the location parameter, by default 0. These are the parameters in the first parameterization.
nu
defines the number of degrees of freedom. Note, alpha takes the limit of abs(beta), and lambda=-nu/2.
x
a numeric vector.
scale
a logical flag, by default TRUE. Should the time series be scaled by its standard deviation to achieve a more stable optimization?
doplot
a logical flag. Should a plot be displayed?
span
x-coordinates for the plot, by default 100 values automatically selected and ranging between the 0.001, and 0.999 quantiles. Alternatively, you can specify the range by an expression like span=seq(min, max, times = n), where, min and max are the left and right endpoints of the range, and n gives the number of the intermediate points.
trace
a logical flag. Should the parameter estimation process be traced?
title
a character string which allows for a project title.
description
a character string which allows for a brief description.
...
parameters to be parsed.

Value

returns a list with the following components:
estimate
the point at which the maximum value of the log liklihood function is obtained.
minimum
the value of the estimated maximum, i.e. the value of the log liklihood function.
code
an integer indicating why the optimization process terminated. 1: relative gradient is close to zero, current iterate is probably solution; 2: successive iterates within tolerance, current iterate is probably solution; 3: last global step failed to locate a point lower than estimate. Either estimate is an approximate local minimum of the function or steptol is too small; 4: iteration limit exceeded; 5: maximum step size stepmax exceeded five consecutive times. Either the function is unbounded below, becomes asymptotic to a finite value from above in some direction or stepmax is too small.
gradient
the gradient at the estimated maximum.
steps
number of function calls.

Details

The function nlm is used to minimize the "negative" maximum log-likelihood function. nlm carries out a minimization using a Newton-type algorithm.

Examples

Run this code
## ghtFit -
   # Simulate Random Variates:
   set.seed(1953)
   
## ghtFit -  
   # Fit Parameters:

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