hyperbFitStart function

Find Starting Values for Fitting a Hyperbolic Distribution

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

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.

Returns

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.

References

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

Barndorff-Nielsen, O., , P., Jensen, J., and , 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.

Author(s)

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

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")