% 
% Written by:
% -- 
% John L. Weatherwax                2006-12-31
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clc; 
close all; clear; 

qj = [ 5     6   1   1   2   2   2   2 ]; qj = qj(:);
pj = [ 0.2 0.2 0.1 0.1 0.1 0.1 0.1 0.1 ]; pj = pj(:);
N  = length(qj);

x0 = ones(1,N-1)/N;
wj = fminsearch( @(x) max_adj_return_fn(x,pj,qj), x0 ); wj = wj(:);

% compute the first N-1 logistic mapped log weights and then the Nth one from all the N-1 others: 
%
lwj = exp( wj )/( 1 + sum(exp(wj)) ); lwj = [ lwj; 1-sum(lwj) ];

lwj % print them

wj = lwj;

% compute the mean and standard deviation: 
%
m = sum( pj .* wj .* ( qj + 1 ) ) - 1 

uncer = sqrt( sum( pj .* ( wj .* ( qj + 1 ) - 1 - m ).^2 ) )