Choice of positive distribution law for nuclear data

Abstract

Nuclear data evaluation files in the ENDF6 format provide mean values and associated uncertainties for physical quantities relevant in nuclear physics. Uncertainties are denoted as Δ in the format description, and are commonly understood as standard deviations. Uncertainties can be completed by covariance matrices. The evaluations do not provide any indication on the probability density function to be used when sampling. Three constraints must be observed: the mean value, the standard deviation and the positivity of the physical quantity. MENDEL code generally uses positively truncated Gaussian distribution laws for small relative standard deviations and a lognormal law for larger uncertainty levels (>50%). Indeed, the use of truncated Gaussian laws can modify the mean and standard deviation value. In this paper, we will make explicit the error in the mean value and the standard deviation when using different types of distribution laws. We also employ the principle of maximum entropy as a criterion to choose among the truncated Gaussian, the fitted Gaussian and the lognormal distribution. Remarkably, the difference in terms of entropy between the candidate distribution laws is a function of the relative standard deviation only. The obtained results provide therefore general guidance for the choice among these distributions.