Environmental hot spots and hot moments (HSHMs) represent rare locations and events that exert disproportionate influence over the environment. While several mechanistic models have been used to characterize HSHMs behavior at specific sites, a critical missing component of research on HSHMs has been the development of clear, conventional statistical models. In this paper, we introduced a novel stochastic framework for analyzing HSHMs and the uncertainties. This framework can easily incorporate heterogeneous features in the spatiotemporal domain and can offer inexpensive solutions for testing future scenarios. The proposed approach utilizes indicator random variables (RVs) to construct a statistical model for HSHMs. The HSHMs indicator RVs are comprised of spatial and temporal components, which can be used to represent the unique characteristics of HSHMs. We identified three categories of HSHMs and demonstrated how our statistical framework are adjusted for each category. The three categories are (1) HSHMs defined only by spatial (static) components, (2) HSHMs defined by both spatial and temporal (dynamic) components, and (3) HSHMs defined by multiple dynamic components. The representation of an HSHM through its spatial and temporal components allows researchers to relate the HSHM’s uncertainty to the uncertainty of its components. We illustrated the proposed statistical framework through several HSHM case studies covering a variety of surface, subsurface, and coupled systems.