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fBasics (version 2110.79)

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.
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 =
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:
  • estimatethe point at which the maximum value of the log liklihood function is obtained.
  • minimumthe value of the estimated maximum, i.e. the value of the log liklihood function.
  • codean 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.
  • gradientthe gradient at the estimated maximum.
  • stepsnumber 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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