Not every long-term deviation from the norm can be considered as a result of a catastrophe. Such occurrences may also be caused by statistically rare events, driven by the internal dynamics, following the true statistics. For a catastrophe, exogenous factors and/or structural changes must be in play. Separating a catastrophe from a statistically rare negative event is fairly important, but at the same time a highly non-trivial task, which is the objective of this study. Our technical approach is motivated by a principle, attributed originally to Pierre-Simon Laplace, which can be stated in words as: “When a rare event occurs, there is a typical way for it to occur. The likelihood of that typical way dominates among the possibly infinitely many ways for that event to occur.” To demonstrate our idea, we provide examples from financial time-series and climate science.