Prove that the auxiliary function Qjn is concavenamely, ????Qjn is convexif we choose all component models in a finite mixture model as one of the

Prove that the auxiliary function Q¹j¹nºº is concave—namely, ????Q¹j¹nºº is convex—if we choose all component models in a finite mixture model as one of the following e-family distributions:

a. Multivariate Gaussian distribution

b. Multinomial distribution

c. Dirichlet distribution

d. von Mises–Fisher distribution