Hospital pharmacy replenishment decisions are made under demand uncertainty, where stockouts may compromise service continuity and overstock may immobilize scarce resources. This study proposes a demand-profile-informed framework for selecting probabilistic inventory models for medication supply decisions. Monthly demand records and consolidated operational cost parameters for 13 medicines over 48 months were analyzed to characterize high-, medium-, low-, and intermittent-demand profiles. Candidate models included normal, gamma, negative binomial type II, and zero-inflated negative binomial distributions. Each fitted distribution was embedded in a two-stage stochastic inventory-cost model, where distribution-specific scenarios determined first-stage replenishment quantities and binary ordering decisions, and second-stage shortage and overstock outcomes were evaluated. A Monte Carlo simulation study assessed model behavior under controlled levels of demand, variability, zero-demand frequency, trend, and shortage-cost exposure. Empirical results showed substantial demand heterogeneity across medicines. Normal and gamma models provided the best statistical fit for most recurrent-demand medicines, whereas zero-inflated negative binomial models dominated several intermittent-demand cases. Model-based replenishment reduced realized costs for 11 of the 13 medicines, with percentage savings ranging from 15.4% to 99.3% among improved cases; however, one medicine showed a negative saving, confirming that statistical fit and operational cost performance may diverge. Simulation results identified zero-demand frequency as the main driver of model selection, with zero-inflated models becoming dominant once zero-demand months were introduced. The proposed framework provides interpretable decision rules to support differentiated, data-driven replenishment decisions in hospital pharmacy management.