gbhill(1) 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 <[email protected]>

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

## COPYRIGHT

Copyright © 2001-2015 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.