Objective function that is minimised in starship estimation method
The starship is a method for fitting the generalised lambda distribution.
See starship for more details.
This function is the objective funciton minimised in the methods. It is a goodness of fit measure carried out on the depths of the data.
starship.obj(par, data, inverse.eps, param = "fmkl")
par |
parameters of the generalised lambda distribution, a vector of
length 4, giving lambda 1 to lambda 4.
See |
data |
Data — a vector |
inverse.eps |
Accuracy of calculation for the numerical determination of F(x), defaults to 1e-8 |
param |
choose parameterisation:
|
The starship method is described in King \& MacGillivray, 1999 (see
references). It is built on the fact that the
generalised lambda distribution (gld)
is a transformation of the uniform distribution. Thus the inverse of this
transformation is the distribution function for the gld. The starship method
applies different values of the parameters of the distribution to the
distribution function, calculates the depths q corresponding to the data
and chooses the parameters that make the depths closest to a uniform
distribution.
The closeness to the uniform is assessed by calculating the Anderson-Darling
goodness-of-fit test on the transformed data against the uniform, for a
sample of size length(data).
The Anderson-Darling goodness of fit measure, computed on the transformed data, compared to a uniform distribution. Note that this is NOT the goodness-of-fit measure of the generalised lambda distribution with the given parameter values to the data.
Robert King, robert.king@newcastle.edu.au, https://tolstoy.newcastle.edu.au/~rking/ Darren Wraith
Freimer, M., Mudholkar, G. S., Kollia, G. & Lin, C. T. (1988), A study of the generalized tukey lambda family, Communications in Statistics - Theory and Methods 17, 3547–3567.
Ramberg, J. S. & Schmeiser, B. W. (1974), An approximate method for generating asymmetric random variables, Communications of the ACM 17, 78–82.
King, R.A.R. & MacGillivray, H. L. (1999), A starship method for fitting the generalised lambda distributions, Australian and New Zealand Journal of Statistics 41, 353–374
Owen, D. B. (1988), The starship, Communications in Statistics - Computation and Simulation 17, 315–323.
data <- rgl(100,0,1,.2,.2) starship.obj(c(0,1,.2,.2),data,inverse.eps=1e-10,"fmkl")
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