Listing A3: Plot the skewed Bhattacharrya divergences between two normal distributions as an equivalent skewed Jensen divergence between two normal distributions.

varalpha(v1,v2,alpha):=(v1*v2)/((1-alpha)*v1+alpha*v2)$ mualpha(mu1,v1,mu2,v2,alpha):=(alpha*mu1*v2+(1-alpha)*mu2*v1)/((1-alpha)*v1+alpha*v2)$ assume(v1>0)$assume(v2>0)$ theta1(mu,v):=mu/v$ theta2(mu,v):=-1/(2*v)$; F(theta1,theta2):=((-theta1**2)/(4*theta2))+(1/2)*log(-%pi/theta2)$ JF(alpha,theta1,theta2,theta1p,theta2p):=alpha*F(theta1,theta2)+(1-alpha)*F(theta1p,theta2p)-F(alpha*theta1+(1-alpha)*theta1p,alpha*theta2+(1-alpha)*theta2p); m1:0;v1:1;m2:1;v2:2; plot2d(JF(alpha,theta1(m1,v1),theta2(m1,v1),theta1(m2,v2),theta2(m2,v2)),[alpha,0,1]);