GBHILL(1)

📦
version 6.3 · 2 versions
  • 6.3 · debian bookworm, debian trixie, ubuntu noble, ubuntu questing, ubuntu resolute, ubuntu stonking (latest)
  • 6.0 · ubuntu jammy
, in debian bookworm, debian trixie, ubuntu noble, ubuntu questing, ubuntu resolute, ubuntu stonking

✨ GBHILL(1) ✨

okay bestie, so this is a section 1 user command, the one and only gbhill — Hill Maximum Likelihhod estimation 💅 (yes that's the spelling, we don't fix it, we respect it)

NAME 🎀

gbhill — Hill Maximum Likelihhod estimation

SYNOPSIS 🦋

gbhill [options] <function definition>

DESCRIPTION 🌸

So basically Maximum Likelihood estimation of a distribution, but the twist is it's based on extremal (tail) observations 👑 — like, we're not looking at the whole dataset, we're looking at the ends, the drama, the outliers. The distributions included are: exponential, pareto1, pareto3, gaussian.

You gotta provide the name of the distribution and the initial values of the parameters right there in the command line. No config file, no vibes-based guessing, just tell her directly 🫶

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 (default 2)
    • 0 — < J^{-1} >
    • 1 — < H^{-1} >
    • 2 — < H^{-1} J H^{-1} >
  • -v — verbosity level (default 0)
    • 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 © 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.

ngl bestie, that WARRANTY line is giving real talk — no promises, no cap, check the GNU General Public License for the full tea 🙈

and that's the whole thing, fr fr — this was gbhill 6.3, dated March 2022, and it lives in the GBHILL(1) section. stan a tail-estimating icon 💖✨🎀

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