NAME

       gbhill - Hill Maximum Likelihhod estimation

SYNOPSIS

       gbhill [options] <function definition>

DESCRIPTION

       Maximum  Likelihood  estimation of distribution based on extremal (tail) observations. The
       distributions included are: exponential, pareto1, pareto3, gaussian. Provide the  name  of
       the distribution and the initial values of the parameters in the command line.

OPTIONS

       -O     type of output (default 0)

       0      parameters and min NLL

       1      parameters and errors

       2      the distribution function

       3      the density function

       4      transformed observations: uniform in [0.1] under the null

       5      Renyi residuals: iid uniform in [0.1] under the null

       -M     method used (default 0)

       0      unconditional, upper tail

       1      threshold, upper tail

       2      unconditional, lower tail

       3      threshold, lower tail

       -V     variance matrix estimation (default2)

       0      < J^{-1} >

       1      < H^{-1} >

       2      < H^{-1} J H^{-1} >

       -v     verbosity level (default0)

       0      just results

       1      comment headers

       2      summary statistics

              3+ minimization steps

       -a     print entire set for -O 1,2

       -u     observations or threshold (default 1)

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

       -h     this help

       -A     comma  separated  MLL optimization options step,tol,iter,eps,msize, algo. Use empty
              fields for default (default 0.01,0.01,100,1e-6,1e-6,5)

       step   initial step size of the searching algorithm

       tol    line search tolerance iter: maximum number of iterations

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

       algo   optimization     methods:     0     Fletcher-Reeves,     1     Polak-Ribiere,     2
              Broyden-Fletcher-Goldfarb-Shanno,    3    Steepest    descent,    4    simplex,   5
              Broyden-Fletcher-Goldfarb-Shanno2.

EXAMPLES

       gbhill pareto1 1 1 < file.dat
              estimate the Pareto type 1 distribution, initial values are gamma=1 and b=1

       gbhill -u .2 pareto1 1 1 < file.dat
              the same using only top 20% observations

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.