Radionuclide stations in the international monitoring system (IMS) network of the Comprehensive Nuclear-Test-Ban Treaty (CTBT) Organization (CTBTO) routinely collect air samples and assess activity concentrations. Activities collected in samples are often caused by emissions from nuclear facilities, but they could also indicate a noble gas release from a nuclear explosion. Characterization of CTBT-relevant nuclear events may use the evolution of isotopic ratios over time, which goes from the release of an assumed nuclear explosion, through atmospheric transport, to sample collection and measurements. This work outlines the statistical hypotheses behind analysis procedures from sample measurements to event characterization. The first hypothesis is to determine whether radioxenon is detected, H0: the null hypothesis of detector background; H1: the alternative of radioxenon detection. The radioxenon is assumed to be detected if the net number of counts is above the decision threshold. The second hypothesis is formulated regarding the radioxenon background at an IMS station: H0, the null hypothesis of normal radioxenon background; H1, the alternative of anomalous radioxenon detection. The abnormal concentration threshold is estimated based on the statistical analysis of the previous samples in a specified period, such as 365 days, resulting in two categories of B and C, while Level A is assigned to samples with no radioxenon detection. Finally, discrimination of a nuclear explosion source against releases of nuclear facilities is based on isotopic ratio analysis, e.g., relationship plots of four or three radioxenon isotopes. Both Level C and B samples in the IDC sample categorization scheme are used. The hypothesis is formulated: H0, the null hypothesis of releases from nuclear facilities; H1, the alternative of nuclear explosion source. The overlap between the discrimination line and lower and upper limits of the coverage interval of isotopic ratios is then tested.