# GHT distribution fit

`dist-ghtFit.Rd`

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.

## Details

The function `nlm`

is used to minimize the "negative"
maximum log-likelihood function. `nlm`

carries out a minimization
using a Newton-type algorithm.

## Value

an object from class `"fDISTFIT"`

.

Slot `fit`

is 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.

## Examples

```
## ghtFit -
# Simulate Random Variates:
set.seed(1953)
## ghtFit -
# Fit Parameters:
```