hyperbFitStart: Find Starting Values for Fitting a Hyperbolic Distribution
In sjp/GeneralizedHyperbolic: The generalized hyperbolic distribution

Description Usage Arguments Details Value Author(s) References See Also Examples

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

  hyperbFitStart(x, breaks = NULL, startValues = "BN",
                 paramStart = NULL, startMethodSL = "Nelder-Mead",
                 startMethodMoM = "Nelder-Mead", ...)
  hyperbFitStartMoM(x, startMethodMoM = "Nelder-Mead", ...)

`x`	Data vector.
`breaks`	Breaks for histogram. If missing, defaults to those generated by `hist(x, right = FALSE, plot = FALSE)`.
`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 `optim`.

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.

hyperbFitStart returns a list with components:

`paramStart`	A vector with elements `mu`, `delta`, `alpha` and `beta` giving the starting value of param.
`xName`	A character string with the actual `x` argument name.
`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.

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

Barndorff-Nielsen, O. (1977) Exponentially decreasing distributions for the logarithm of particle size, Proc. Roy. Soc. Lond., A353, 401–419.

Barndorff-Nielsen, O., Bl<c3><a6>sild, P., Jensen, J., and S<c3><b6>renson, 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.

dhyperb, dskewlap, hyperbFit, hist, and optim.

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