gigFit: Fit the Generalized Inverse Gausssian Distribution to Data

Description

Fits a generalized 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

gigFit(x, freq = NULL, paramStart = NULL,
         startMethod = c("Nelder-Mead","BFGS"),
         startValues = c("LM","GammaIG","MoM","Symb","US"),
         method = c("Nelder-Mead","BFGS","nlm"),
         stand = TRUE, plots = FALSE, printOut = FALSE,
         controlBFGS = list(maxit = 200),
         controlNM = list(maxit = 1000),
         maxitNLM = 1500, ...)

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

Value

gigFit returns a list with components:

param: A vector giving the maximum likelihood estimate of param, as c(chi, psi, lambda).
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.
obs: The data used to fit the generalized inverse Gaussian distribution.
obsName: A character string with the actual x argument name.
paramStart: Starting value of param returned by call to gigFitStart.
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.

Arguments

x: Data vector for gigFit. Object of class "gigFit" for print.gigFit and plot.gigFit.
freq: A vector of weights with length equal to length(x).
paramStart: A user specified starting parameter vector param taking the form c(chi, psi, lambda).
startMethod: Method used by gigFitStartMoM in calls to optim.
startValues: Code giving the method of determining starting values for finding the maximum likelihood estimate of param.
method: Different optimisation methods to consider. See Details.
stand: Logical. If TRUE, the data is first standardized by dividing by the sample standard deviation.
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.
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 optim, par, hist, logHist, qqgig and ppgig.
object: Object of class "gigFit" for coef.gigFit and for vcov.gigFit.

Author

David Scott d.scott@auckland.ac.nz, David Cusack

Details

Possible values of the argument startValues are the following:

"LM": Based on fitting linear models to the upper tails of the data x and the inverse of the data 1/x.
"GammaIG": Based on fitting gamma and inverse gamma distributions.
"MoM": Method of moments.
"Symb": Not yet implemented.
"US": User-supplied.

If startValues = "US" then a value must be supplied for paramStart.

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

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

Jörgensen, B. (1982). Statistical Properties of the Generalized Inverse Gaussian Distribution. Lecture Notes in Statistics, Vol. 9, Springer-Verlag, New York.

Examples

Run this code

param <- c(1, 1, 1)
dataVector <- rgig(500, param = param)
## See how well gigFit works
gigFit(dataVector)
##gigFit(dataVector, plots = TRUE)

## See how well gigFit works in the limiting cases
## Gamma case
dataVector2 <- rgamma(500, shape = 1, rate = 1)
gigFit(dataVector2)

## Inverse gamma
require(actuar)
dataVector3 <- rinvgamma(500, shape = 1, rate = 1)
gigFit(dataVector3)

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

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