starship                 package:gld                 R Documentation

_C_a_r_r_y _o_u_t _t_h_e "_s_t_a_r_s_h_i_p" _e_s_t_i_m_a_t_i_o_n _m_e_t_h_o_d _f_o_r _t_h_e _g_e_n_e_r_a_l_i_s_e_d
_l_a_m_b_d_a _d_i_s_t_r_i_b_u_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     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.

_U_s_a_g_e:

     starship(data, optim.method = "Nelder-Mead", initgrid = NULL, param="FMKL",
     optim.control=NULL)

_A_r_g_u_m_e_n_t_s:

    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 of lambda 3)  and
          'ldvect' (a vector of values of lambda 4).   If it is left as
          NULL, these both default to

            -1.5  -1  -.5  -.1  0  .1  .2  .4  .8  1  1.5

   param: choose parameterisation:  'fmkl' uses _Freimer, Mudholkar,
          Kollia and Lin (1988)_ (default). 'rs' uses _Ramberg and
          Schmeiser (1974)_

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. 

_D_e_t_a_i_l_s:

     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.

_V_a_l_u_e:

     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

_A_u_t_h_o_r(_s):

     Robert King, robert.king@newcastle.edu.au, <URL:
     http://maths.newcastle.edu.au/~rking/>

     Darren Wraith, Darren.Wraith@studentmail.newcastle.edu.au

_R_e_f_e_r_e_n_c_e_s:

     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.

     <URL: http://maths.newcastle.edu.au/~rking/gld/>

_S_e_e _A_l_s_o:

     'starship.adaptivegrid',  'starship.obj'

_E_x_a_m_p_l_e_s:

     data <- rgl(100,0,1,.2,.2)
     starship(data,optim.method="Nelder-Mead",initgrid=list(lcvect=(0:4)/10,
     ldvect=(0:4)/10))

