hyperbFitStart function

Find Starting Values for Fitting a Hyperbolic Distribution

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

Arguments

  • 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 .
  • ThetaStart: Starting values for Theta 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.

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 ThetaStart.

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: - ThetaStart: A vector with elements pi, lZeta (log of zeta), lDelta (log of delta), and mu giving the starting value of Theta.

  • 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 pi, lZeta (log of zeta), lDelta (log of delta), and mu.

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

HyperbolicDistribution, dskewlap, hyperbFit, hist, and optim.

Examples

Theta <- c(2,2,2,2)
dataVector <- rhyperb(500,Theta)
hyperbFitStart(dataVector,startValues="FN")
hyperbFitStartMoM(dataVector)
hyperbFitStart(dataVector,startValues="MoM")
HyperbolicDist packageRead PDF manual