A multivariate generalization of the exponential dispersion family (4.14) is f(y i ; i , )

A multivariate generalization of the exponential dispersion family (4.14) is f(y_i; θ_i, ϕ) = exp{[y_i’ θ_i – b(θ_i)]/α(ϕ) + c(y_i, ϕ)}, where θ_i is the natural parameter. Show that the multinomial variate y_i defined in Section 7.1.5 for a single trial with parameters {π_j, j = 1,..., j – 1} is the (J – 1)-parameter exponential family, with baseline-category logits as natural parameters.