Representing and Approximating Symmetric and Asymmetric Probability Coverage Intervals by Possibility Distributions

At the application level, it is important to be able to define, around the measurement result, an interval that will contain an important part of the distribution of the measured values, that is, a coverage interval. This practice, which is acknowledged by the ISO Guide, is a major shift from the probabilistic representation. It can be viewed as a probability-possibility transformation by viewing possibility distributions as encoding coverage intervals. In this paper, we extend previous works by proposing exact and approximate closed-form possibility expressions of optimum coverage intervals associated with continuous symmetric and asymmetric unimodal probability densities. The approximation is useful in finding bounds on p-values for common statistical tests for key comparison measurements.