GBHILL

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		< Jˆ{-1} >
	1		< Hˆ{-1} >
	2		< Hˆ{-1} J Hˆ{-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 <gbutils@googlegroups.com>

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.