gigFit: Fit the Generalized Inverse Gausssian Distribution to Data

In GeneralizedHyperbolic: The Generalized Hyperbolic Distribution

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 class 'gigFit'
print(x,
        digits = max(3, getOption("digits") - 3), ...)

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

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

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.

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.

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.

Author(s)

David Scott [e-mail], David Cusack

References

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

See Also

optim, par, hist, logHist (pkg DistributionUtils), qqgig, ppgig, and gigFitStart.

Examples

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")

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