Paper detail

Influence of statistics on the measured moments of conserved quantities in relativistic heavy ion collisions

We study statistics dependence of the probability distributions and the means of measured moments of conserved quantities, respectively. The required statistics of all interested moments and their products are estimated based on a simple simulation. We also explain why the measured moments are underestimated when the statistics are insufficient.With the statistics at RHIC/BES, the second and third order moments can be reliably obtained based on the method of Centrality bin width correction (CBWC), which can not be applied for the fourth order moments at low energy. With planning statistics at RHIC/BES II, and improved CBWC method, $κσ^2$ in a finer centrality bin scale should be measurable. This will help us to understand the current observation of energy and centrality dependence of high-order moments.