Fit of a Normal Inverse Gaussian Distribution

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 
#>