---
name: "gbhill"
section: "1"
platform: "linux"
package: "gbutils"
version: "6.3-1+b1"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/gbhill"
---

# gbhill(1)

Hill Maximum Likelihhod estimation

## 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 \<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.