Discrete probability distributions in nuclear reactor noise

Abstract

A presentation is given of recent contributions that reactor noise analysis brought up to the theory of probability and its applications, in terms of new profiles and distribution families. A time documentary approach is adopted. The well-known PMZBB (Pal-Mogilner-Zolotukhin-Bell-Babala) distribution, Türkcan and Dragt's first try to derive the probability profile from the generating function and Routti Szeless and Ruby's elegant computational procedure—based on the partitions of integer numbers—are progressively recalled. In search of new probability distributions approximating the PMZBB profile, a number of generating functions have been introduced, analyzed and mutually compared by the authors of this paper. These functions lead to: (1) the Logarithmic distribution, (2) the Radical distribution, (3) the Algebraic distribution, (4) the Poisson-Logarithmic distribution, (5) the Poisson-Radical distribution and (6) the Poisson-Algebraic distribution. Distribution (4) is also known as Polya or Pascal or Negative Binomial distribution. Distributions (2) (3) (5) and (6) are an absolute novelty in the field of probability theory. Distributions (4) (5) and (6) belong to the class of ’generalized Poisson distributions’, introduced by Gurland some years ago.