hyperbFitStart {GeneralizedHyperbolic}

Find Starting Values for Fitting a Hyperbolic Distribution

Description

Finds starting values for input to a maximum likelihood routine for fitting hyperbolic distribution to data.

Usage

  hyperbFitStart(x, startValues = c("BN","US","FN","SL","MoM"),
                 paramStart = NULL,
                 startMethodSL = c("Nelder-Mead","BFGS"),
                 startMethodMoM = c("Nelder-Mead","BFGS"), ...)
  hyperbFitStartMoM(x, startMethodMoM = "Nelder-Mead", ...)

Arguments

x

Data vector.

startValues

Vector of the different starting values to consider. See Details.

paramStart

Starting values for param if startValues = "US".

startMethodSL

Method used by call to optim in finding skew Laplace estimates.

startMethodMoM

Method used by call to optim in finding method of moments estimates.

...

Passes arguments to hist and optim.

Details

Possible values of the argument startValues are 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.

If startValues = "US" then a value must be supplied for paramStart.

If startValues = "MoM", hyperbFitStartMoM is called. These starting values are based on Barndorff-Nielsen et al (1985).

If startValues = "SL", or startValues = "MoM" an initial optimisation is needed to find the starting values. These optimisations call optim.

Value

hyperbFitStart returns a list with components:

paramStart

A vector with elements mu, delta, alpha and beta giving the starting value of param.

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.

hyperbFitStartMoM returns only the method of moments estimates as a vector with elements mu, delta, alpha and beta.

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.

Barndorff-Nielsen, O., Blæsild, P., Jensen, J., and Sörenson, M. (1985). The fascination of sand. In A celebration of statistics, The ISI Centenary Volume, eds., Atkinson, A. C. and Fienberg, S. E., pp. 57–87. New York: Springer-Verlag.

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

See Also

dhyperb, dskewlap, hyperbFit, hist, and optim.

Examples

param <- c(2, 2, 2, 1)
dataVector <- rhyperb(500, param = param)
hyperbFitStart(dataVector, startValues = "FN")
hyperbFitStartMoM(dataVector)
hyperbFitStart(dataVector, startValues = "MoM")