GeneralizedHyperbolic (version 0.8-4)

hyperbFitStart: 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.

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.

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.

References

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

Barndorff-Nielsen, O., Bl<e6>sild, P., Jensen, J., and S<U+001B296E>son, 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

# NOT RUN {
param <- c(2, 2, 2, 1)
dataVector <- rhyperb(500, param = param)
hyperbFitStart(dataVector, startValues = "FN")
hyperbFitStartMoM(dataVector)
hyperbFitStart(dataVector, startValues = "MoM")
# }