GeneralizedHyperbolic: gigFit – R documentation

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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 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")

GeneralizedHyperbolic

The Generalized Hyperbolic Distribution

v0.8-4

GPL (>= 2)

Authors

David Scott <d.scott@auckland.ac.nz>

Initial release

2018-05-15