Carry out the “starship” estimation method for the generalised lambda distribution using a grid-based search
Calculates estimates for the generalised lambda
distribution on the basis of data, using the starship method.
The starship method is built on the fact that the
generalised lambda distribution (gld)
is a transformation of the uniform distribution. This method finds the
parameters that transform the data closest to the uniform distribution.
This function uses a grid-based search.
starship.adaptivegrid(data, initgrid,inverse.eps = 1e-08, param="FMKL")
data |
Data to be fitted, as a vector |
initgrid |
A list with elements,
|
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).
This function carries out a grid-based search. This was the original method
of King \& MacGillivray, 1999, but you are advised to instead use
starship which uses a grid-based search together with an
optimisation based search.
See GeneralisedLambdaDistribution for details on
parameterisations.
response |
The minimum “response value” — the result of the internal goodness-of-fit measure. This is the return value of starship.obj. See King \& MacGillivray, 1999 for more details |
lambda |
A vector of length 4 giving the values of lambda 1 to lambda 4 that produce this minimum response, i.e. the estimates |
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.adaptivegrid(data,list(lcvect=(0:4)/10,ldvect=(0:4)/10))
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