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## [5b02c4]: inst / quotapanning.m Maximize Restore History

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81``` ```## Copyright (C) 2009 Esteban Cervetto ## ## 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 ## . ## -*- 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 ## ## @verbatim ## E[Z(i,k) ] ## B(k) = ------------ ## E[Z(i,0) ] ## @end verbatim ## ## holds for all k = @{0, @dots{}, n-1@} and for all i = @{1, @dots{}, m@}. ## Z represents the incremental losses; then losses satisfy ## Z(k) = (S(k) - S(k-1) ),Z(0) = S(0) for all i = @{1, @dots{}, m@}. ## ## @var{quotas} returns a row vector with the cumulative quotas. The transformation ## from incremental ratios to cumulative quotas is: ## ## @verbatim ## l=k ## E B(l) ## l=0 ## quotas(k) = ----------- ## l=n-1 ## E B(l) ## l=0 ## @end verbatim ## ## @seealso {bferguson, ultimatepanning, quotald, quotaad, quotamack} ## @end deftypefn 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 ```