R: Fit the Normal Laplace Distribution to Data

nlFit {NormalLaplace}

R Documentation

Fit the Normal Laplace Distribution to Data

Description

Fits a 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.

Usage

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

Arguments

`x`	Data vector for `nlFit`.
`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)`.
`startMethod`	Method used by `nlFitStart` 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 `"nlFit"` for `print.nlFit`, `plot.nlFit`, `coef.nlFit` and `vcov.nlFit`.
`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`, `qqnl` and `ppnl`. For the `print`, `coef` and `vcov` methods this parameter has no effect.

Details

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

Value

A list with components:

`param`	A vector giving the maximum likelihood estimate of parameters, as `c(mu, sigma, alpha, beta)`.
`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 `nlFitStart`.
`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`.

Author(s)

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

Examples

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

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

[Package NormalLaplace version 0.3-1 Index]