WGPDFIT_ML Internal routine for wgpdfit (ML estimates for GPD data) CALL: [f,k,s] = wgpdfit_ml(x,data) f = function values. k = shape parameter of GPD. s = scale parameter of GPD. This function is used by wgpdfit for numerical solution of the ML estimate, i.e. solve f=0 for x. data = wgpdrnd(0.3,1,0,200,1); x_ML = fzero('wgpdfit_ml',0,[],data); [f,k_ML,s_ML] = wgpdfit_ml(x_ML,data) % Estimates k_ML and s_ML See also wgpdfit
Quick test of the routines in module 'cycles' | |
Parameter estimates for Generalized Pareto data |
001 function [f,k,s] = wgpdfit_ml(x,data) 002 %WGPDFIT_ML Internal routine for wgpdfit (ML estimates for GPD data) 003 % 004 % CALL: [f,k,s] = wgpdfit_ml(x,data) 005 % 006 % f = function values. 007 % k = shape parameter of GPD. 008 % s = scale parameter of GPD. 009 % 010 % This function is used by wgpdfit for numerical solution of 011 % the ML estimate, i.e. solve f=0 for x. 012 % data = wgpdrnd(0.3,1,0,200,1); 013 % x_ML = fzero('wgpdfit_ml',0,[],data); 014 % [f,k_ML,s_ML] = wgpdfit_ml(x_ML,data) % Estimates k_ML and s_ML 015 % 016 % See also wgpdfit 017 018 % References 019 % 020 % Davidson & Smith (1990) 021 % Models for Exceedances over high Threholds. 022 % Journal of the Royal Statistical Society B,52, pp. 393-442. 023 024 % Tested on; Matlab 5.3 025 % History: 026 % Created by PJ 22-Jun-2000 027 % Revised by PJ 10-Oct-2000 028 % - Help text added w* 029 030 % In order to avoid boundary problems in numerical solution we use a transformation 031 % Transformation: x = log(1/max_data - t), -Inf < t < 1/max_data 032 % Inverse Trans.: t = 1/max(data) - exp(x), -Inf < x < Inf 033 034 t = 1/max(data) - exp(x); % Inverse Transformation 035 036 N = length(data); 037 038 k = -1/N*sum(log(1-t*data)); % Shape parameter 039 s = k/t; % Scale parameter 040 041 % Evaluate function 042 f = (1/k-1)*sum(data./(1-t*data)) - N/t; 043
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