Listing A5: Calculate symbolically the Kullback–Leibler divergence and the Bhattacharyya coefficient between a half normal distribution and an exponential distribution.

assume(sigma>0); halfnormal(x,sigma):=(sqrt(2)/(sqrt(%pi*sigma**2)))*exp(-x**2/(2*sigma**2)); assume(lambda>0); exponential(x,lambda):=lambda*exp(-lambda*x); /* KLD diverges */ integrate(exponential(x,lambda)*log(exponential(x,lambda)/halfnormal(x,sigma)),x,0,inf); /* KLD converges */ integrate(halfnormal(x,sigma)*log(halfnormal(x,sigma)/exponential(x,lambda)),x,0,inf); /* Bhattacharyya coefficient */ assume(alpha>0); assume(alpha<1); integrate( (halfnormal(x,sigma)**alpha) * (exponential(x,lambda)**(1-alpha)),x,0,inf);