THE MULTIPARAMETRIC EXPONENTIAL FAMILIES WITH QUADRATIC COVARIANCE-MATRIX FUNCTIONS

For multiparametric regular exponential family with parameters m=E₀x, we point out that for polynomial covariance functions with k order case （P（k）VF-REF）, its Bhattacharyya natrix has a simple form: the submatrices B（i, j）=0 for j＞（k-1） （i-1） +1, i=1, 2, …, and conversely, if B（2, i）=0 for all i≥k＞2, then this REF is P（k）VF-REF.Thus for k≤2 （QVE-REF） case, allthe submatrices are zeno matrices besides the diagonal submatrices for which the recurrence expressions are given.In the last part of this papen, we discussed the distribution types for multiparametric QVF-REF, many of them are natural extension of the single parametric QVF-REF case.