nigFitStart function

Find Starting Values for Fitting a normal inverse Gaussian Distribution

Find Starting Values for Fitting a normal inverse Gaussian Distribution

Finds starting values for input to a maximum likelihood routine for fitting normal inverse Gaussian distribution to data.

nigFitStart(x, startValues = c("FN","Cauchy","MoM","US"),
              paramStart = NULL,
              startMethodMoM = c("Nelder-Mead","BFGS"), ...)
  nigFitStartMoM(x, startMethodMoM = "Nelder-Mead", ...)

Arguments

  • x: data vector.
  • startValues: a character strin specifying the method for starting values to consider. See Details .
  • paramStart: starting values for param if startValues = "US".
  • 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.
  • "FN": A fitted normal distribution.
  • "Cauchy": Based on a fitted Cauchy distribution, from fitdistr() of the list("MASS") package.
  • "MoM": Method of moments.

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

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

Returns

nigFitStart 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.

nigFitStartMoM 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 , Christine Yang Dong

See Also

dnig, dskewlap, nigFit, hist, optim, fitdistr.

Examples

param <- c(2, 2, 2, 1)
dataVector <- rnig(500, param = param)
nigFitStart(dataVector, startValues = "FN")
nigFitStartMoM(dataVector)
nigFitStart(dataVector, startValues = "MoM")
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