nigFit: Fit the normal inverse Gaussian Distribution to Data

In GeneralizedHyperbolic: The Generalized Hyperbolic Distribution

Fit the normal inverse Gaussian Distribution to Data

Description

Fits a normal inverse Gaussian distribution to data. Displays the histogram, log-histogram (both with fitted densities), Q-Q plot and P-P plot for the fit which has the maximum likelihood.

Usage

  nigFit(x, freq = NULL, paramStart = NULL,
         startMethod = c("Nelder-Mead","BFGS"),
         startValues = c("FN","Cauchy","MoM","US"),
         criterion = "MLE",
         method = c("Nelder-Mead","BFGS","nlm",
                   "L-BFGS-B","nlminb","constrOptim"),
         plots = FALSE, printOut = FALSE,
         controlBFGS = list(maxit = 200),
         controlNM = list(maxit = 1000), maxitNLM = 1500,
         controlLBFGSB = list(maxit = 200),
         controlNLMINB = list(),
         controlCO = list(), ...)

  ## S3 method for class 'nigFit'
print(x,
        digits = max(3, getOption("digits") - 3), ...)

  ## S3 method for class 'nigFit'
plot(x, which = 1:4,
       plotTitles = paste(c("Histogram of ","Log-Histogram of ",
                            "Q-Q Plot of ","P-P Plot of "), x$obsName,
                          sep = ""),
       ask = prod(par("mfcol")) < length(which) & dev.interactive(), ...)

  ## S3 method for class 'nigFit'
coef(object, ...)

  ## S3 method for class 'nigFit'
vcov(object, ...)

Arguments

x	Data vector for nigFit. Object of class "nigFit" for print.nigFit and plot.nigFit.
freq	A vector of weights with length equal to length(x).
paramStart	A user specified starting parameter vector param taking the form c(mu, delta, alpha, beta).
startMethod	Method used by nigFitStart in calls to optim.
startValues	Code giving the method of determining starting values for finding the maximum likelihood estimate of param.
criterion	Currently only "MLE" is implemented.
method	Different optimisation methods to consider. See Details.
plots	Logical. If FALSE suppresses printing of the histogram, log-histogram, Q-Q plot and P-P plot.
printOut	Logical. If FALSE suppresses printing of results of fitting.
controlBFGS	A list of control parameters for optim when using the "BFGS" optimisation.
controlNM	A list of control parameters for optim when using the "Nelder-Mead" optimisation.
maxitNLM	A positive integer specifying the maximum number of iterations when using the "nlm" optimisation.
controlLBFGSB	A list of control parameters for optim when using the "L-BFGS-B" optimisation.
controlNLMINB	A list of control parameters for nlminb when using the "nlminb" optimisation.
controlCO	A list of control parameters for constrOptim when using the "constrOptim" optimisation.
digits	Desired number of digits when the object is printed.
which	If a subset of the plots is required, specify a subset of the numbers 1:4.
plotTitles	Titles to appear above the plots.
ask	Logical. If TRUE, the user is asked before each plot, see par(ask = .).
...	Passes arguments to par, hist, logHist, qqnig and ppnig.
object	Object of class "nigFit" for coef.nigFit and for vcov.nigFit.

Details

startMethod can be either "BFGS" or "Nelder-Mead".

startValues can be one of the following:

"US"

User-supplied.

"FN"

A fitted normal distribution.

"Cauchy"

Based on a fitted Cauchy distribution.

"MoM"

Method of moments.

For the details concerning the use of paramStart, startMethod, and startValues, see nigFitStart.

The three optimisation methods currently available are:

"BFGS"

Uses the quasi-Newton method "BFGS" as documented in optim.

"Nelder-Mead"

Uses an implementation of the Nelder and Mead method as documented in optim.

"nlm"

Uses the nlm function in R.

For details of how to pass control information for optimisation using optim and nlm, see optim and nlm.

When method = "nlm" is used, warnings may be produced. These do not appear to be a problem.

Value

A list with components:

param	A vector giving the maximum likelihood estimate of param, as c(mu, delta, alpha, beta).
maxLik	The value of the maximised log-likelihood.
method	Optimisation method used.
conv	Convergence code. See the relevant documentation (either optim or nlm) for details on convergence.
iter	Number of iterations of optimisation routine.
x	The data used to fit the normal inverse Gaussian distribution.
xName	A character string with the actual x argument name.
paramStart	Starting value of param returned by call to nigFitStart.
svName	Descriptive name for the method finding start values.
startValues	Acronym for the method of finding start values.
breaks	The cell boundaries found by a call to hist.
midpoints	The cell midpoints found by a call to hist.
empDens	The estimated density found by a call to hist.

Author(s)

David Scott [e-mail], Christine Yang Dong

References

Barndorff-Nielsen, O. (1977) Exponentially decreasing distributions for the logarithm of particle size, Proc. Roy. Soc. Lond., A353, 401–419.

Fieller, N. J., Flenley, E. C. and Olbricht, W. (1992) Statistics of particle size data. Appl. Statist., 41, 127–146.

Paolella, Marc S. (2007) Intermediate Probability: A Computational Approach, Chichester: Wiley

See Also

optim, nlm, par, hist, logHist, qqnig, ppnig, dskewlap and nigFitStart.

Examples

param <- c(2, 2, 2, 1)
dataVector <- rnig(500, param = param)
## See how well nigFit works
nigFit(dataVector)
nigFit(dataVector, plots = TRUE)
fit <- nigFit(dataVector)
par(mfrow = c(1, 2))
plot(fit, which = c(1, 3))

## Use nlm instead of default
nigFit(dataVector, method = "nlm")

GeneralizedHyperbolic documentation built on Nov. 26, 2023, 5:07 p.m.