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gbhill - Online in the Cloud

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This is the command gbhill that can be run in the OnWorks free hosting provider using one of our multiple free online workstations such as Ubuntu Online, Fedora Online, Windows online emulator or MAC OS online emulator

PROGRAM:

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 Renyi residuals: iid uniform in [0.1] 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

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