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We first examine the basic calculations, which are then implemented in the m-procedure jointzw .
% file jdemo7.m
P = [0.061 0.030 0.060 0.027 0.009;0.015 0.001 0.048 0.058 0.013;
0.040 0.054 0.012 0.004 0.013;0.032 0.029 0.026 0.023 0.039;
0.058 0.040 0.061 0.053 0.018;0.050 0.052 0.060 0.001 0.013];X = -2:2;
Y = -2:3;jdemo7 % Call for data in jdemo7.m
jcalc % Used to set up calculation matrices t, u- - - - - - - - - -
H = u.^2 % Matrix of values for W = h(X,Y)H =
9 9 9 9 94 4 4 4 4
1 1 1 1 10 0 0 0 0
1 1 1 1 14 4 4 4 4
G = abs(t) % Matrix of values for Z = g(X,Y)G =2 1 0 1 2
2 1 0 1 22 1 0 1 2
2 1 0 1 22 1 0 1 2
2 1 0 1 2[W,PW] = csort(H,P) % Determination of marginal for WW = 0 1 4 9
PW = 0.1490 0.3530 0.3110 0.1870[Z,PZ] = csort(G,P) % Determination of marginal for ZZ = 0 1 2
PZ = 0.2670 0.3720 0.3610r = W(3) % Third value for W
r = 4s = Z(2) % Second value for Z
s = 1
To determine , we need to determine the positions for which this pair of values is taken on. By inspection, we find these to be (2,2), (6,2), (2,4), and (6,4). Then is the total probability at these positions. This is 0.001 + 0.052 + 0.058 + 0.001 = 0.112. We put this probability in the jointprobability matrix at the position. This may be achieved by MATLAB with the following operations.
[i,j] = find((H==W(3))&(G==Z(2))); % Location of (t,u) positions
disp([i j]) % Optional display of positions
2 26 2
2 46 4
a = find((H==W(3))&(G==Z(2))); % Location in more convenient form
P0 = zeros(size(P)); % Setup of zero matrixP0(a) = P(a) % Display of designated probabilities in P
P0 =0 0 0 0 0
0 0.0010 0 0.0580 00 0 0 0 0
0 0 0 0 00 0 0 0 0
0 0.0520 0 0.0010 0PZW = zeros(length(W),length(Z)) % Initialization of PZW matrix
PZW(3,2) = total(P(a)) % Assignment to PZW matrix withPZW = 0 0 0 % W increasing downward
0 0 00 0.1120 0
0 0 0
PZW = flipud(PZW) % Assignment with W increasing upward
PZW =0 0 0
0 0.1120 00 0 0
0 0 0
The procedure
jointzw carries out this operation for each possible pair of
W and
Z values (with the
flipud operation coming only after all individual assignments are made).
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