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 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=list(
lcvect = c(-1.5, -1, -0.5, -0.1, 0, 0.1, 0.2, 0.4, 0.8, 1, 1.5),
ldvect = c(-1.5, -1, -0.5, -0.1, 0, 0.1, 0.2, 0.4, 0.8, 1, 1.5),
levect = c(-0.5,-0.25,0,0.25,0.5)),param="FMKL")
The minimum ``response value'' --- the result of the internal goodness-of-fit measure. This is the return value of starship.obj. See King and MacGillivray, 1999 for more details
A vector of length 4 giving the values of \(\lambda_1\) to \(\lambda_4\) that produce this minimum response, i.e. the estimates
Data to be fitted, as a vector
A list with elements,
lcvect, a vector of values for \(\lambda_3\),
ldvect, a vector of values for \(\lambda_4\) and
levect, a vector of values for \(\lambda_5\)
(levect is only required if param is fm5).
Note: if param=rs, the non-positive values are dropped from
lcvect and ldvect.
choose parameterisation:
fmkl uses Freimer, Mudholkar, Kollia and Lin (1988) (default).
rs uses Ramberg and Schmeiser (1974)
fm5 uses the 5 parameter version of the FMKL parameterisation
(paper to appear)
Robert King, Darren Wraith
The starship method is described in King and MacGillivray, 1999 (see references). It is built on the fact that the generalised lambda distribution 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 and MacGillivray, 1999, but you are advised to instead use
starship which uses a grid-based search together with an
optimisation based search.
See references for details on parameterisations.
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.
starship,
starship.obj
# \donttest{
data <- rgl(100,0,1,.2,.2)
starship.adaptivegrid(data,list(lcvect=(0:4)/10,ldvect=(0:4)/10))
# }Run the code above in your browser using DataLab