hyperbFit: Fit the Hyperbolic Distribution to Data

Description

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.

Usage

hyperbFit(x, freq = NULL, breaks = NULL, ThetaStart = 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 hyperbFit
print(x,
        digits = max(3, getOption("digits") - 3), ...)
  # S3 method for 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(), ...)

Value

A list with components:

Theta: A vector giving the maximum likelihood estimate of Theta, as (pi,zeta,delta,mu).
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.
ThetaStart: Starting value of Theta returned by call to hyperbFitStart.
svName: Descriptive name for the method finding start values.
startValues: Acronym for the method of finding start values.
KNu: Value of the Bessel function in the fitted density.
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.

Arguments

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).
ThetaStart: A user specified starting parameter vector Theta taking the form c(pi,zeta,delta,mu).
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 Theta.
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.

Author

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

Details

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 ThetaStart, 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.

References

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.

Examples

Run this code

Theta <- c(2,2,2,2)
dataVector <- rhyperb(500, Theta)
## 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")

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