NAME

       gbepfit - Fit a symmetric power exponential density

SYNOPSIS

       gbepfit [options]

DESCRIPTION

       Fit symmetric power exponential density using maximum-likelihood or the method of moments.

OPTIONS

       -O     output type (default 0)

       0      parameter b a m and log-likelihood

       1      the estimated distribution function computed on the provided points

       2      the estimated density function computed on the provided points

       3      parameters b a m and their standard errors

       -x     set initial conditions b,a,m  (default 2,1,0)

       -m     the mode is not estimated but is set to the value provided

       -s     number of intervals to explore at each iteration (default 10)

       -V     verbosity level (default 0)

       0      just the final result

       1      headings and summary table

       2      intermediate steps results

       3      intermediate steps internals

       4+     details of optim. routine

       -M     active estimation steps. The value is the sum of (default 7)

       1      initial estimation based on method of moments

       2      global optimization not considering lack of smoothness in m

       4      local optimization taking non-smoothness in m into consideration

       -G     set  global  optimization  options. Fields are step,tol,iter,eps,msize,algo.  Empty
              field implies default (default .1,1e-2,100,1e-3,1e-5,3)

       -I     set local optimization options.  Fields  are  step,tol,iter,eps,msize,algo.   Empty
              field implies default (default .01,1e-4,200,1e-4,1e-5,5)

       -F     input fields separators (default " \t")

       -h     this help

       The optimization parameters are step  initial step size of the searching algorithm

       tol    line search tolerance iter: maximum number of iterations

       eps    gradient tolerance : stopping criteria ||gradient||<eps

       msize  simplex max size : stopping criteria ||max edge||<msize

       algo   optimization     methods:     0     Fletcher-Reeves,     1     Polak-Ribiere,     2
              Broyden-Fletcher-Goldfarb-Shanno, 3 Steepest  descent,  4  Nelder-Mead  simplex,  5
              Broyden-Fletcher-Goldfarb-Shanno  v.2,  6 Nelder-Mead simplex ver. 2, 7 Nelder-Mead
              simplex rnd init.

EXAMPLES

       gbepfit -m 1 -M 6 <file
              estimate a and b with m=1 and skipping initial method of moments estimation

AUTHOR

       Written by Giulio Bottazzi

REPORTING BUGS

       Report bugs to <gbutils@googlegroups.com>

       Package home page <http://cafim.sssup.it/~giulio/software/gbutils/index.html>

COPYRIGHT

       Copyright © 2001-2018 Giulio Bottazzi This program is free software; you can  redistribute
       it  and/or  modify  it  under  the  terms of the GNU General Public License (version 2) as
       published by the Free Software Foundation;

       This program is distributed in the hope that it will be useful, but WITHOUT ANY  WARRANTY;
       without  even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
       See the GNU General Public License for more details.