On the Distribution of the Estimated Coherence

The recent paper by Abdelfattah and Nicolas proposed a novel coherence magnitude estimator and studied its properties. Here, we derive simpler and more explicit expressions for four of the properties that were studied: 1) the probability density function; 2) moments; 3) Mellin transform; and 4) second-kind moments. We establish numerical efficiency of these expressions and provide simple Maple programs for inversion. We expect that the results presented here could enhance applicability of the new estimator.