gbhill(1)

Usage

gbhill [options] <function definition>

Overview

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

Releases

5 releases since Debian 9 (Stretch); the text changed 3 times.