Bo-Cox for multivariate normalization

[robmio]

Good morning, everyone. I must solve the following “optimization” problem: I have a matrix of n=6 rows and p=2 columns:

M9:=[[1,4],[2,8],[7,12],[8,16],[15,21],[19,3]]

Assuming that the following matrix is not distributed according to the multivariate normal, there is the Box-Cox method to normalize the matrix. Box and Cox (1964) present the family of transformations defined by:

Z = M9(i,j)^L(j) if L<>0
Z = ln(M9(i,j)) if L(j) = 0

where, in this case, L(j):=[L1,L2]. The precise criterion for transforming to multivariate normality is to find the collection of transformations L(j):=[L1,L2] such that the function:


F(L) = (-n/2)*ln(ABS(S(L)))+Σ((L(j)-1)*Σ(ln(M9(i,j)),i,1,n),j,1,p)


is maximized. It is therefore a question of maximizing F(L).
Can anyone help me? Thanks so much