  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 behaviour of different measures of dependence and
derive maximum likelihood estimates when all nodes are observed and when the
inner node is hidden.
