hyperbFit {HyperbolicDist}

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 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(), ...)

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.

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.

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.

Author(s)

David Scott [e-mail], Ai-Wei Lee, Jennifer Tso, Richard Trendall, Thomas Tran

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.

See Also

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

Examples

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")