  Probabilistic forecasts comprehensively describe the uncertainty in the
unknown future outcome, making them essential for decision making and risk
management. While several methods have been introduced to evaluate
probabilistic forecasts, existing evaluation techniques are ill-suited to the
evaluation of tail properties of such forecasts. However, these tail properties
are often of particular interest to forecast users due to the severe impacts
caused by extreme outcomes. In this work, we introduce a general notion of tail
calibration for probabilistic forecasts, which allows forecasters to assess the
reliability of their predictions for extreme outcomes. We study the
relationships between tail calibration and standard notions of forecast
calibration, and discuss connections to peaks-over-threshold models in extreme
value theory. Diagnostic tools are introduced and applied in a case study on
European precipitation forecasts
