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gbhill - Hill Maximum Likelihhod estimation


gbhill [options] <function definition>


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.


-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


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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