Generalized extreme value analysis of criticality tallies in Monte Carlo calculation

Abstract

Generalized extreme value (GEV) is the standard statistical model on the occurrences of extreme observations. The trinity theorem in GEV asserts that properly normalized maxima from blocks of data converge in distribution to one of the Weibull, Gumbel and Fréchet distributions as the data size increases. In this work, the methodology of GEV is applied to criticality tallies in Monte Carlo fission source cycles in order to evaluate the utility value of the distribution tail ends. Numerical results obtained under a sufficiently large number of particles per cycle show that the extreme value index (EVI) in GEV is not capable of being differentiated for the upper and lower distribution tail ends of criticality tallies. It is also shown that the EVI of criticality tallies falls within the range of Weibull distribution including the EVI of Gumbel distribution as the role of a boundary value layer. As a demonstration aimed at practicality, GEV is utilized for the population diagnosis under an insufficient number of particles per cycle. It turns out that the transition from one equilibrium to other equilibrium due to small population size makes the EVIs of upper and lower distribution tail ends depart from each other so that one of them falls in the range of Weibull distribution and the other in that of Fréchet distribution.