hyperbFit: Fit the Hyperbolic Distribution to Data
In sjp/GeneralizedHyperbolic: The generalized hyperbolic distribution

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

Fits a hyperbolic 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.

  hyperbFit(x, freq = NULL, breaks = NULL, paramStart = NULL,
            startMethod = "Nelder-Mead", startValues = "BN",
            method = "Nelder-Mead", hessian = FALSE,
            plots = FALSE, printOut = FALSE,
            controlBFGS = list(maxit = 200),
            controlNM = list(maxit = 1000), maxitNLM = 1500, ...)

  ## S3 method for class 'hyperbFit'
print(x,
        digits = max(3, getOption("digits") - 3), ...)

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

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

`x`	Data vector for `hyperbFit`. Object of class `"hyperbFit"` for `print.hyperbFit` and `plot.hyperbFit`.
`freq`	A vector of weights with length equal to `length(x)`.
`breaks`	Breaks for histogram, defaults to those generated by `hist(x, right = FALSE, plot = FALSE)`.
`paramStart`	A user specified starting parameter vector param taking the form `c(mu, delta, alpha, beta)`.
`startMethod`	Method used by `hyperbFitStart` 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.
`hessian`	Logical. If `TRUE` the value of the hessian is returned.
`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 `par`, `hist`, `logHist`, `qqhyperb` and `pphyperb`.
`object`	Object of class `"hyperbFit"` for `coef.hyperbFit` and for `vcov.hyperbFit`.

startMethod can be either "BFGS" or "Nelder-Mead".

startValues can be one of the following:

"US"User-supplied.
"BN"Based on Barndorff-Nielsen (1977).
"FN"A fitted normal distribution.
"SL"Based on a fitted skew-Laplace distribution.
"MoM"Method of moments.

For the details concerning the use of paramStart, startMethod, and startValues, see hyperbFitStart.

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.

A list with components:

`param`	A vector giving the maximum likelihood estimate of param, as `c(mu, delta, alpha, beta)`.
`maxLik`	The value of the 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 of optimisation routine.
`x`	The data used to fit the hyperbolic distribution.
`xName`	A character string with the actual `x` argument name.
`paramStart`	Starting value of param returned by call to `hyperbFitStart`.
`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`.

David Scott d.scott@auckland.ac.nz, Ai-Wei Lee, Jennifer Tso, Richard Trendall, Thomas Tran

Barndorff-Nielsen, O. (1977) Exponentially decreasing distributions for the logarithm of particle size, Proc. Roy. Soc. Lond., A353, 401–419.

Fieller, N. J., Flenley, E. C. and Olbricht, W. (1992) Statistics of particle size data. Appl. Statist., 41, 127–146.

optim, nlm, par, hist, logHist, qqhyperb, pphyperb, dskewlap and hyperbFitStart.

param <- c(2, 2, 2, 1)
dataVector <- rhyperb(500, param = param)
## See how well hyperbFit works
hyperbFit(dataVector)
hyperbFit(dataVector, plots = TRUE)
fit <- hyperbFit(dataVector)
par(mfrow = c(1, 2))
plot(fit, which = c(1, 3))

## Use nlm instead of default
hyperbFit(dataVector, method = "nlm")