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+## Copyright (C) 2009 Esteban Cervetto <estebancster@gmail.com>
+##
+## Octave is 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.
+##
+## Octave 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.
+##
+## You should have received a copy of the GNU General Public License
+## along with Octave; see the file COPYING.  If not, see
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{quotas} =} quotapanning (@var{s})
+## Calculate the cumulative quotas by the Panning method.
+##
+## @var{s} is a mxn matrix that contains the run-off triangle, where m is the number of accident-years
+## and n is the number of periods to final development. @var{s} may contain u = m-n complete years.
+## The value @var{s}(i,k), 1<=i<=m, 0<=k<=n-1 represents the cumulative losses from accident-period i
+## settled with a delay of at most k years. 
+## The values @var{s}(i,k) with i + k > m must be zero because is future time. 
+##
+## The Panning method asumes that exists a development pattern on the incremental ratios.
+## This means that the identity 
+## @group
+## @example
+##          E[Z(i,k) ]
+## B(k) =  ------------
+##          E[Z(i,0) ]
+## @end example
+## @end group
+## holds for all k = {0,...,n-1} and for all i = {1,...,m}. 
+## Z represents the incremental losses; then losses satisfy 
+## Z(k) = (S(k) - S(k-1) ),Z(0) = S(0) for all i = {1,...,m}.
+##
+## @var{quotas} returns a row vector with the cumulative quotas. The transformation
+## from incremental ratios to cumulative quotas is:
+## @group
+## @example
+##                    l=k  
+##                     E    B(l)
+#                     l=0   
+## @var{quotas}(k) =  -----------
+##                   l=n-1    
+##                     E    B(l)
+##                    l=0     
+## @end example
+## @end group
+##
+## @seealso {bferguson, ultimatepanning, quotald, quotaad, quotamack}
+## @end deftypefn
+
+## Author: Act. Esteban Cervetto ARG <estebancster@gmail.com>
+##
+## Maintainer: Act. Esteban Cervetto ARG <estebancster@gmail.com>
+##
+## Created: jul-2009
+##
+## Version: 1.1.0 
+##
+## Keywords: actuarial reserves insurance bornhuetter ferguson chainladder
+
+function quotas = quotapanning (S)
+
+[m,n] = size (S);           #triangle with m years (i=1,2,u,...u+1,u+2,....m) and n periods (k=0,1,2,...n-1)
+u = m - n;                                     #rows of the upper square
+S = fliplr(triu(fliplr(S),-u));                   #ensure S is triangular  
+
+# calculate Z
+Z = [S(:,1), S(:,2:n)-S(:,1:n-1)];
+Z = fliplr(triu(fliplr(Z),-u));        #clean Z
+
+# calc empirical values of the incremental factors
+B = Z ./ (Z * [ones(n,1),zeros(n,n-1)]');
+ 
+# weights Z(i,0)^2/Z(0)^2
+ W = repmat((Z(:,1).^2),1,n);          #numerator
+ W =fliplr(triu(fliplr(W),-u));        #clean low triangle
+ a = repmat(sum(W),m,1);               #denominator
+ a = fliplr(triu(fliplr(a),-u));       #clean low triangle
+ W = W./a; #divido
+ W = fliplr(triu(fliplr(W),-u));       #clean low triangle
+
+# Pannings incremental factors
+B_Pan  = diag(B' * W)';                #weighted product
+quotas = cumsum(porcentual(B_Pan));    #cumulated quota
+ 
+end

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