R: Fit the Generalized Inverse Gausssian Distribution to Data

gigFit {GeneralizedHyperbolic}

R Documentation

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

References

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

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")

[Package GeneralizedHyperbolic version 0.8-6 Index]