In the age of cloud, Grid, P2P, and volunteer distributed computing, large-scale systems with tens of thousands of unreliable hosts are increasingly common. Invariably, these systems are composed of heterogeneous hosts whose individual availability often exhibit different statistical properties (for example stationary versus nonstationary behavior) and fit different models (for example exponential, Weibull, or Pareto probability distributions). In this paper, we describe an effective method for discovering subsets of hosts whose availability have similar statistical properties and can be modeled with similar probability distributions. We apply this method with about 230,000 host availability traces obtained from a real Internet-distributed system, namely SETI@home. We find that about 21 percent of hosts exhibit availability, that is, a truly random process, and that these hosts can often be modeled accurately with a few distinct distributions from different families. We show that our models are useful and accurate in the context of a scheduling problem that deals with resource brokering. We believe that these methods and models are critical for the design of stochastic scheduling algorithms across large systems where host availability is uncertain.