nigFit function

Fit the normal inverse Gaussian Distribution to Data

Fit the normal inverse Gaussian Distribution to Data

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.

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.

Returns

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.

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

Author(s)

David Scott d.scott@auckland.ac.nz , Christine Yang Dong

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")
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