gbhill - Hill Maximum Likelihhod estimation

       Written by Giulio Bottazzi

       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.

gbhill 6.3                                         March 2022                                          GBHILL(1)

       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.

       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

       gbhill - Hill Maximum Likelihhod estimation

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

       6      Renyi residuals: iid exponential with mean 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.

       Report bugs to <gbutils@googlegroups.com>

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

gbhill [options] <functiondefinition>