  We theoretically derive the probability densities of the entanglement
measures of a pure non-ergodic many-body state, represented in a bipartite
product basis and with its reduced density matrix described by a generalized,
multi-parametric Wishart ensemble with unit trace. Our results indicate
significant fluctuations of the measures around their average behavior
(specifically for the states away from separability and maximum entanglement
limits). The information is relevant not only for hierarchical arrangement of
entangled states (e.g., revealing the flaws in their characterization based on
average behavior) but also for phase transition studies of many body systems.
