Abstract

In astrophysics, the C statistics, a likelihood ratio statistic, has been widely adopted for model fitting and goodness-of-fit assessments for Poisson-count data with heterogeneous rates. It is well known that when the sample size is large, the C statistics enjoy desirable theoretical properties. However, in high-energy physics, the observations are very sparse, making the theoretical properties of C statistics questionable. Over the past decade, researchers have gradually realized the problems of directly applying the C statistics for such small count data and published approximate solutions. We give a comprehensive study of the properties of C statistics and evaluate various algorithms for goodness-of-fit assessment using C statistics, emphasizing the low-count scenarios. Theoretical results, computational algorithms, extensive simulation studies, and real data applications will be presented.