.\" DO NOT MODIFY THIS FILE!  It was generated by help2man 1.47.3.
.TH GBHILL "1" "March 2018" "gbhill 5.7.1" "User Commands"
.SH NAME
gbhill \- Hill Maximum Likelihhod estimation
.SH SYNOPSIS
.B gbhill
[\fI\,options\/\fR] \fI\,<function definition>\/\fR
.SH 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.
.SH OPTIONS
.TP
\fB\-O\fR
type of output (default 0)
.TP
0
parameters and min NLL
.TP
1
parameters and errors
.TP
2
the distribution function
.TP
3
the density function
.TP
4
transformed observations: uniform in [0.1] under the null
.TP
5
Renyi residuals: iid uniform in [0.1] under the null
.TP
\fB\-M\fR
method used (default 0)
.TP
0
unconditional, upper tail
.TP
1
threshold, upper tail
.TP
2
unconditional, lower tail
.TP
3
threshold, lower tail
.TP
\fB\-V\fR
variance matrix estimation (default2)
.TP
0
< J^{\-1} >
.TP
1
< H^{\-1} >
.TP
2
< H^{\-1} J H^{\-1} >
.TP
\fB\-v\fR
verbosity level (default0)
.TP
0
just results
.TP
1
comment headers
.TP
2
summary statistics
.IP
3+ minimization steps
.TP
\fB\-a\fR
print entire set for \fB\-O\fR 1,2
.TP
\fB\-u\fR
observations or threshold (default 1)
.TP
\fB\-F\fR
input fields separators (default " \et")
.TP
\fB\-h\fR
this help
.TP
\fB\-A\fR
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)
.TP
step
initial step size of the searching algorithm
.TP
tol
line search tolerance iter: maximum number of iterations
.TP
eps
gradient tolerance : stopping criteria ||gradient||<eps
.TP
algo
optimization methods: 0 Fletcher\-Reeves, 1 Polak\-Ribiere,
2 Broyden\-Fletcher\-Goldfarb\-Shanno, 3 Steepest descent,
4 simplex, 5 Broyden\-Fletcher\-Goldfarb\-Shanno2.
.SH EXAMPLES
.TP
gbhill pareto1 1 1 < file.dat
estimate the Pareto type 1 distribution,
initial values are gamma=1 and b=1
.TP
gbhill \-u .2 pareto1 1 1 < file.dat
the same using only top 20% observations
.SH AUTHOR
Written by Giulio Bottazzi
.SH "REPORTING BUGS"
Report bugs to <gbutils@googlegroups.com>
.PP
.br
Package home page <http://cafim.sssup.it/~giulio/software/gbutils/index.html>
.SH COPYRIGHT
Copyright \(co 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;
.PP
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.