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 d.scott@auckland.ac.nz,
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")
Results
R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> library(HyperbolicDist)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/HyperbolicDist/hyperbFit.Rd_%03d_medium.png", width=480, height=480)
> ### Name: hyperbFit
> ### Title: Fit the Hyperbolic Distribution to Data
> ### Aliases: hyperbFit print.hyperbFit plot.hyperbFit
> ### Keywords: distribution
>
> ### ** Examples
>
> Theta <- c(2,2,2,2)
> dataVector <- rhyperb(500, Theta)
> ## See how well hyperbFit works
> hyperbFit(dataVector)
Data: dataVector
Parameter estimates:
pi zeta delta mu
8.3910 2.4766 0.6017 0.6877
Likelihood: -1416.444
Method: Nelder-Mead
Convergence code: 1
Iterations: 1001
> hyperbFit(dataVector, plots = TRUE)
Data: dataVector
Parameter estimates:
pi zeta delta mu
8.3910 2.4766 0.6017 0.6877
Likelihood: -1416.444
Method: Nelder-Mead
Convergence code: 1
Iterations: 1001
> fit <- hyperbFit(dataVector)
> par(mfrow = c(1,2))
> plot(fit, which = c(1,3))
>
> ## Use nlm instead of default
> hyperbFit(dataVector, method = "nlm")
Data: dataVector
Parameter estimates:
pi zeta delta mu
245.79919 2.55299 0.02118 0.54571
Likelihood: -1416.394
Method: nlm
Convergence code: 1
Iterations: 675
Warning messages:
1: In nlm(llfunc, ThetaStart, hessian = hessian, iterlim = maxitNLM, :
NA/Inf replaced by maximum positive value
2: In nlm(llfunc, ThetaStart, hessian = hessian, iterlim = maxitNLM, :
NA/Inf replaced by maximum positive value
>
>
>
>
>
>
> dev.off()
null device
1
>