Non-Poissonian particle fluctuations in the cosmic ray extensive air shower and shower size estimation

In this paper we analyse the particle density fluctuations recorded by the cosmic ray Extensive Air Shower array and their influence on the estimation of the shower parameters. The calculations were based on simulations using the CORSIKA program. We compared our results with measurements performed at Walailak University using a small shower array installed there as part of the CREDO-Maze project. This comparison confirmed the validity of our theoretical predictions. We show that the simple assumption of the independence of shower particles is not valid even for showers containing a large number of particles. We describe the particle density fluctuations in terms of a negative binomial distribution. We show that the proposed change in the nature of the fluctuations has implications for shower size estimation.