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
-
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.
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 © 2001-2018 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.