ISO/TR 13587:2012 is concerned with three basic statistical approaches for the evaluation and interpretation of measurement uncertainty: the frequentist approach including bootstrap uncertainty intervals, the Bayesian approach, and fiducial inference. The common feature of these approaches is a clearly delineated probabilistic interpretation or justification for the resulting uncertainty intervals. For each approach, the basic method is described and the fundamental underlying assumptions and the probabilistic interpretation of the resulting uncertainty are discussed. Each of the approaches is illustrated using two examples including an example from the ISO/IEC Guide 98-3 (Uncertainty of measurement - Part 3: Guide to the expression of uncertainty in measurement (GUM:1995)). This document also includes a discussion of the relationship between the methods proposed in GUM Supplement 1 and these three statistical approaches.