starship {gld} | R Documentation |
Calculates estimates for the FMKL parameterisation of 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 to find a suitable starting point (using
starship.adaptivegrid
) then uses optim
to find
the parameters that do this.
starship(data, optim.method = "Nelder-Mead", initgrid = NULL, inverse.eps = 1e-08, param="FMKL", optim.control=NULL)
data |
Data to be fitted, as a vector | |||||||||||||||||||||||||||||||||
optim.method |
Optimisation method for optim to use,
defaults to Nelder-Mead | |||||||||||||||||||||||||||||||||
initgrid |
Grid of values of lambda 3 and
lambda 4
to try, in starship.adaptivegrid . This should be 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 ).
If it is left as NULL, the default grid depends on the parameterisation. For fmkl , both lcvect and ldvect default to:
levect is NULL).
For rs , both lcvect and ldvect default to:
levect is NULL).
For fm5 , both lcvect and ldvect default to:
levect defaults to:
| |||||||||||||||||||||||||||||||||
inverse.eps |
Accuracy of calculation for the numerical determination of F(x), defaults to 1e-8 | |||||||||||||||||||||||||||||||||
param |
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) | |||||||||||||||||||||||||||||||||
optim.control |
List of options for the optimisation step. See
optim for details. If left as NULL, the parscale
control is set to scale lambda 1
and lambda 2 by the absolute value of their starting points.
|
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 {em 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 is implemented in 2 stages in this function. First a grid search is
carried out, over a small number of possible parameter values
(see starship.adaptivegrid
for details). Then the minimum from
this search is given as a starting point for an optimisation of the
Anderson-Darling value using optim, with method given by optim.method
See GeneralisedLambdaDistribution
for details on
parameterisations.
Returns a list, with
lambda |
A vector of length 4, giving the estimated parameters, in order, lambda 1 - location parameter lambda 2 - scale parameter lambda 3 - first shape parameter lambda 4 - second shape parameter |
grid.results |
output from the grid search - see
starship.adaptivegrid for details |
optim |
output from the optim search -
optim for details |
Robert King, robert.king@newcastle.edu.au, http://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.
http://tolstoy.newcastle.edu.au/~rking/gld/
starship.adaptivegrid
,
starship.obj
data <- rgl(100,0,1,.2,.2) starship(data,optim.method="Nelder-Mead",initgrid=list(lcvect=(0:4)/10, ldvect=(0:4)/10))