Some problems in the characterization of the wishart distribution

الملخص EN

Under the multivariate linear model{Y , Xb ,åÄV }, A number of characterization of the distribution of i X have been made based on the properties of the statistics 1 Y and 2 Y when 1 Y and 2 Y be two linear functions defined on R1 as follows n n Y = a X + ....+ a X 1 1 1 and n n Y = b X + .....+ b X 2 1 1 .

Generalizations of these problems to the multivariate case have been made by several authors by extending the techniques used in the univariate case.

In my paper I shall consider some other generalization, which possibly require development of new techniques ,if 1 2 X , X be independent and identically distributed p-vector r.v.,s such that ( \ ) 0 1 2 1 2 E X - AX X + B¢X = ,where A and B are nonsingular matrices.

In special case when A = B-1 , A is symmetric and the egen values do not take values ±1.

Under these conditions that 1 X has an m.n.d.

in the present paper we shall consider a few other cases.