Transformation of Bimodal Probability Distributions Into Possibility Distributions

At the application level, it is important to be able to define the measurement result as an interval that will contain an important part of the distribution of the measured values, that is, a coverage interval. This practice acknowledged by the International Organization for Standardization (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 on unimodal distributions by proposing a possibility representation of bimodal probability distributions. Indeed, U-shaped distributions or Gaussian mixture distribution are not very rare in the context of physical measurements. Some elements to further propagate such bimodal possibility distributions are also exposed. The proposed method is applied to the case of three independent or positively correlated C-grade resistors in series and compared with the Guide to the Expression of Uncertainty in Measurement (GUM) and Monte Carlo methods.