# Fit of a Normal Inverse Gaussian Distribution

`dist-nigFit.Rd`

Estimates the parameters of a normal inverse Gaussian distribution.

## Usage

```
nigFit(x, alpha = 1, beta = 0, delta = 1, mu = 0,
method = c("mle", "gmm", "mps", "vmps"), scale = TRUE, doplot = TRUE,
span = "auto", trace = TRUE, title = NULL, description = NULL, ...)
```

## Arguments

- alpha, beta, delta, mu
The parameters are

`alpha`

,`beta`

,`delta`

, and`mu`

:

shape parameter`alpha`

; skewness parameter`beta`

,`abs(beta)`

is in the range (0, alpha); scale parameter`delta`

,`delta`

must be zero or positive; location parameter`mu`

, by default 0. These is the meaning of the parameters in the first parameterization`pm=1`

which is the default parameterization selection. In the second parameterization,`pm=2`

`alpha`

and`beta`

take the meaning of the shape parameters (usually named)`zeta`

and`rho`

. In the third parameterization,`pm=3`

`alpha`

and`beta`

take the meaning of the shape parameters (usually named)`xi`

and`chi`

. In the fourth parameterization,`pm=4`

`alpha`

and`beta`

take the meaning of the shape parameters (usually named)`a.bar`

and`b.bar`

.- description
a character string which allows for a brief description.

- doplot
a logical flag. Should a plot be displayed?

- method
a character string. Either

`"mle"`

, Maximum Likelihood Estimation, the default,`"gmm"`

Gemeralized Method of Moments Estimation,`"mps"`

Maximum Product Spacings Estimation, or`"vmps"`

Minimum Variance Product Spacings Estimation.- scale
a logical flag, by default

`TRUE`

. Should the time series be scaled by its standard deviation to achieve a more stable optimization?- 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.- title
a character string which allows for a project title.

- trace
a logical flag. Should the parameter estimation process be traced?

- x
a numeric vector.

- ...
parameters to be parsed.

## Value

an object from class `"fDISTFIT"`

.

Slot `fit`

is a list, whose components depend on the method. See
`"fDISTFIT"`

for the meaning of the most common
ones.

Here is an **informal** list of components for the various methods:

for mle: `par`

, `scale`

, `estimate`

, `minimum`

, `code`

plus components from `nlminb()`

plus additions from `.distStandardErrors()`

;

for gmm: only `estimate`

;

for mps and vmps: `estimate`

, `minimum`

, `error`

(s.e.'s), `code`

.

## Examples

```
## Simulate Random Variates
set.seed(1953)
s <- rnig(n = 1000, alpha = 1.5, beta = 0.3, delta = 0.5, mu = -1.0)
nigFit(s, alpha = 1, beta = 0, delta = 1, mu = mean(s), doplot = TRUE,
trace = FALSE)
#> Warning: NaNs produced
#>
#> Title:
#> Normal Inverse Gaussian Parameter Estimation
#>
#> Call:
#> .nigFit.mle(x = x, alpha = alpha, beta = beta, delta = delta,
#> mu = mu, scale = scale, doplot = doplot, span = span, trace = trace,
#> title = title, description = description)
#>
#> Model:
#> Normal Inverse Gaussian Distribution
#>
#> Estimated Parameter(s):
#> alpha beta delta mu
#> 1.6959724 0.3597793 0.5601027 -1.0446402
#>
```