gnlFit: Fit the Generalised Normal Laplace Distribution to Data
In sjp/NormalLaplace: The Normal Laplace Distribution

Description Usage Arguments Details Value Author(s) See Also Examples

Fits a Generalised Normal Laplace 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.

  gnlFit(x, freq = NULL, breaks = "FD", paramStart = NULL,
         startMethod = "Nelder-Mead",
         startValues = c("MoM", "US"),
         method = c("Nelder-Mead", "BFGS", "L-BFGS-B",
                    "nlm", "nlminb"),
         hessian = FALSE,
         plots = FALSE, printOut = FALSE,
         controlBFGS = list(maxit = 200),
         controlLBFGSB = list(maxit = 200),
         controlNLMINB = list(),
         controlNM = list(maxit = 1000),
         maxitNLM = 1500, ...)
  ## S3 method for class 'gnlFit'
print(x, digits = max(3, getOption("digits") - 3), ...)
  ## S3 method for class 'gnlFit'
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 'gnlFit'
coef(object, ...)
  ## S3 method for class 'gnlFit'
vcov(object, ...)

`x`	Data vector for `gnlFit`.
`freq`	A vector of weights with length equal to `length(x)`.
`breaks`	Breaks for plotted histogram, defaults to those generated by `hist(x, right = FALSE, plot = FALSE)`.
`paramStart`	A user specified starting parameter vector taking the form `c(mu, sigma, alpha, beta, rho)`.
`startMethod`	Method used by `gnlFitStart` in calls to `optim`.
`startValues`	Code giving the method of determining starting values for finding the maximum likelihood estimate of the parameters.
`method`	Different optimisation methods to consider. See Details.
`hessian`	Logical. If `TRUE` the value of the Hessian is returned.
`plots`	Logical. If `FALSE` the printing of the histogram, log-histogram, Q-Q plot and P-P plot are suppressed.
`printOut`	Logical. If `FALSE` the printing of the results of fitting will be suppressed.
`controlBFGS`	A list of control parameters for `optim` when using the `"BFGS"` method of optimisation.
`controlLBFGSB`	A list of control parameters for `optim` when using the `"L-BFGS-B"` method of optimisation.
`controlNLMINB`	A list of control parameters for `optim` when using the `"nlminb"` method of optimisation.
`controlNM`	A list of control parameters for `optim` when using the `"Nelder-Mead"` method of optimisation.
`maxitNLM`	A positive integer specifying the maximum number of iterations that are to be undertaken when using the `"nlm"` method of optimisation.
`object`	Object of class `"gnlFit"` for `print.gnlFit`, `plot.gnlFit`, `coef.gnlFit` and `vcov.gnlFit`.
`digits`	Desired number of digits to be shown when the object is printed.
`which`	If a subset of the plots if required, specify a subset of the numbers `1:4`.
`plotTitles`	Titles to appear as the main title above the plots.
`ask`	Logical. If `TRUE`, the user is asked before each plot, see `par(ask = .)`.
`...`	Passes arguments to `par`, `hist`, `logHist`, `qqgnl` and `ppgnl`. For the `print`, `coef` and `vcov` methods this parameter has no effect.

Because the GNL does not have a closed form expression for its density function it leads to slow and less accurate evaluation of the density function. This affects the fitting function which attempts to maximise the likelihood using the density function. Therefore caution is advised as fitting is unstable.

startMethod must be "Nelder-Mead".

startValues can only be "MoM" when using the Method of Moments for estimation, or "US" for user-supplied parameters. For details regarding the use of paramStart, startMethod and startValues, see nlFitStart.

Three optimisation methods are available for use:

"BFGS"Uses the quasi-Newton method "BFGS" as documented in optim.
"L-BFGS-B"Uses the constrained method "L-BFGS-B" 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.
"nlminb"Uses the nlminb function in R, with constrained parameters.

For details on how to pass control information for optimisation using optim and nlm, see optim and nlm.

When method = "nlm" or method = "nlminb" is used, warnings may be produced. However, these do not appear to be problematic.

A list with components:

`param`	A vector giving the maximum likelihood estimate of parameters, as `c(mu, sigma, alpha, beta, rho)`.
`maxLik`	The value of maximised log-likelihood.
`hessian`	If `hessian` was set to `TRUE`, the value of the Hessian. Not present otherwise.
`method`	Optimisation method used.
`conv`	Convergence code. See the relevant documentation (either `optim` or `nlm`) for details on convergence.
`iter`	Number of iterations made by the optimisation routine.
`obs`	The data used to fit the normal Laplace distribution.
`obsName`	A character vector with the actual `x` argument name.
`paramStart`	Starting value of parameters returned by call to `gnlFitStart`.
`svName`	Descriptive name for the method of 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`.

David Scott d.scott@auckland.ac.nz, Simon Potter

optim, nlm, par, hist, logHist, qqgnl, ppgnl, dgnl and gnlFitStart.

param <- c(0, 2, 1, 1, 1)
dataVector <- rgnl(1000, param = param)

## Let's see how well gnlFit works
gnlFit(dataVector)
gnlFit(dataVector, plots = TRUE)
fit <- gnlFit(dataVector)
par(mfrow = c(1, 2))
plot(fit, which = c(1, 3))  # See only histogram and Q-Q plot