Dear all,
I have the following problem, I am looking for the n_ij in this table and I know the N_i
X/Y
Y_Cate1
Y_Cate2
total
X_Cate1
n_11
n_12
N_1
X_Cate2
n_21
n_22
N_2
Total
N_3
N_4
T
I have N_1,N_2,N3 et N_4, and I want to compute n_11, n_12, n_21 n_22
I can write the problem as follows:
1*n_11+1* n_12+0* n_21+0* n_22 = N_1
0* n_11 +0* n_12+1* n_21+1* n_22=N_2
1*n_11+0* n_12+1* n_21+0* n_22 = N_3
0*n_11+1* n_12+0* n_21+1* n_22 = N_4
Matrix A is:
1 1 0 0
A= 0 0 1 1
1 0 1 0
0 1 0 1
V = (n11,n12,n21,n22)' U =(N_1,N2,N3,N4)'
So we have AV =U, if B is the inverse of A or it generalised inverse then
V = B U
I am looking for B
The problem can be view as : How to compute a joint distribution with marginal are known, in a frequency table?
Thank you for any suggestion
Adel
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