We complete the study of the model introduced in [11]. It is a two-color urn
model with multiple drawing and random (non-balanced) time-dependent
reinforcement matrix. The number of sampled balls at each time-step is random.
We identify the exact rates at which the number of balls of each color grows to
infinity and define two strongly consistent estimators for the limiting
reinforcement averages. Then we prove a Central Limit Theorem, which allows to
design a statistical test for such averages.Comment: arXiv admin note: text overlap with arXiv:2102.0628