GeneralizedHyperbolic (version 0.8-4)

nigFit: 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 nigFit
print(x,
        digits = max(3, getOption("digits") - 3), ...)
  # S3 method for 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 nigFit
coef(object, ...)
  # S3 method for 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.

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.

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.

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

# NOT RUN {
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")

# }