Fit the Hyperbolic Distribution to Data
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, paramStart = NULL, startMethod = c("Nelder-Mead","BFGS"), startValues = c("BN","US","FN","SL","MoM"), criterion = "MLE", method = c("Nelder-Mead","BFGS","nlm", "L-BFGS-B","nlminb","constrOptim"), plots = FALSE, printOut = FALSE, controlBFGS = list(maxit = 200), controlNM = list(maxit = 1000), maxitNLM = 1500, controlLBFGSB = list(maxit = 200), controlNLMINB = list(), controlCO = list(), ...) ## 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).
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.
criterion: Currently only "MLE" is implemented.
method: Different optimisation methods to consider. See Details .
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.
controlLBFGSB: A list of control parameters for optim when using the "L-BFGS-B" optimisation.
controlNLMINB: A list of control parameters for nlminb
when using the "nlminb" optimisation.
controlCO: A list of control parameters for constrOptim
when using the "constrOptim" 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 six 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.
"L-BFGS-B": Uses the quasi-Newton method with box constraints "L-BFGS-B" as documented in optim.
"nlminb": Uses the nlminb function in R.
"constrOptim": Uses the constrOptim
function in R.
For details of how to pass control information for optimisation using
optim, nlm, nlminb and constrOptim, see
optim, nlm, nlminb and constrOptim.
When method = "nlm" is used, warnings may be produced. These do not appear to be a problem.
hyperbFit returns 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.
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.
obs: The data used to fit the hyperbolic distribution.
obsName: 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.
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.
David Scott d.scott@auckland.ac.nz , Ai-Wei Lee, Jennifer Tso, Richard Trendall, Thomas Tran, Christine Yang Dong
optim, nlm, nlminb, constrOptim, par, hist, logHist (pkg list("DistributionUtils")), 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")