Binary distributions of concentric rings

We introduce families of jointly symmetric, binary distributions that are generated over directed star graphs whose nodes represent variables and whose edges indicate positive dependences. The families are parametrized in terms of a single parameter. It is an outstanding feature of these distributions that joint probabilities relate to evenly spaced concentric rings. Kronecker product characterizations make them computationally attractive for a large number of variables.We study the behavior of differentmeasures of dependence and derivemaximum likelihood estimateswhen all nodes are observed andwhen the inner node is hidden. © 2014 Elsevier Inc. All rights reserved.