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 BottazziREPORTING 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.