starship.adaptivegrid {gld}

Carry out the “starship” estimation method for the generalised lambda distribution using a grid-based search

Description

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.

Usage

starship.adaptivegrid(data, initgrid,inverse.eps = 1e-08, param="FMKL")

Arguments

data

Data to be fitted, as a vector

initgrid

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). The parameter values given in initgrid are not checked with gl.check.lambda.

inverse.eps

Accuracy of calculation for the numerical determination of F(x), defaults to 10^{-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)

Details

The starship method is described in King and 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 and 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.

Value

response

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

lambda

A vector of length 4 giving the values of \lambda_1 to \lambda_4 that produce this minimum response, i.e. the estimates

Author(s)

Robert King, [e-mail], https://github.com/newystats/

Darren Wraith

References

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.

https://github.com/newystats/gld/

See Also

starship, starship.obj

Examples

data <- rgl(100,0,1,.2,.2)
starship.adaptivegrid(data,list(lcvect=(0:4)/10,ldvect=(0:4)/10))