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function [imfl,imfh,imfl1,imfh1, imfmedian] = demarw(xpo,xprob)
% [imfl,imfh,imfl1,imfh1] = fn_demarw(xpo,xprob)
% Demarcate the .68 and .90 error bands given positions and properly scaled probabilities (weights).
% Calls fn_histwpdfg() first.
%
% xpo: ndraws-by-n. Centered position
% xprob: ndraws-by-n. Must be properly scaled probabilities corresponding to xpo.
%-----------------
% imfl: lower .90 bound, n-by-1
% imfh: higher .90 bound, n-by-1
% imfl1: lower .68 bound, n-by-1
% imfh1: higher .68 bound, n-by-1
% imfmedian: .50 estimate, n-by-1.
%
% Note: fn_histwpdfg() must be called first to get xpo and xprob.
% August 1999 Tao Zha; Revised, August 2000
%
% Copyright (C) 1997-2012 Tao Zha
%
% This free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% It is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% If you did not received a copy of the GNU General Public License
% with this software, see <http://www.gnu.org/licenses/>.
%
[ndraws,n]=size(xpo);
%$$$ .68 and .95 probability bands
imfl = zeros(n,1); % preallocating
imfh = zeros(n,1); % preallocating
imfl1 = zeros(n,1); % preallocating
imfh1 = zeros(n,1); % preallocating
imfmedian = zeros(n,1); % preallocating
imfpo = zeros(4,n); % 4 positions: l,h,l1,h1.
%
%tic
tem = cumsum(xprob); % cumulative probability
tem = tem .* 100;
%
%@@@ the following operations are valid only because tem are increasing!
for k = 1:n
%
%@@@ the following operations are valid only because tem are increasing!
%** 5% low tail
if isempty(max(find(tem(:,k)<5)))
imfl(k) = xpo(1,k);
else
imfl(k) = xpo(max(find(tem(:,k)<5)),k);
end
%** 16% low tail
if isempty(max(find(tem(:,k)<16)))
imfl1(k) = xpo(1,k);
else
imfl1(k) = xpo(max(find(tem(:,k)<16)),k);
end
%** 50% estimate
if isempty(max(find(tem(:,k)<50)))
imfmedian(k) = xpo(1,k);
else
imfmedian(k) = xpo(max(find(tem(:,k)<50)),k);
end
%** 5% high tail
imfh(k) = xpo(min(find(tem(:,k)>95)),k);
%** 16% low tail
imfh1(k) = xpo(min(find(tem(:,k)>84)),k);
end
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