Dependence structures and asymptotic properties of Baker's distributions with fixed marginals

We investigate the properties of Baker's (2008) bivariate distributions with fixed marginals and their multivariate extensions. The properties include the weak convergence to the Fréchet-Hoeffding upper bound, the product-moment convergence, as well as the dependence structures TP2 (totally positive of order 2), or MTP2 (multivariate TP2). In proving the weak convergence, a generalized local limit theorem for binomial distribution is provided.