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, $kappasigma^2$ 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.
By the generator of the UrQMD model, event statistics for the products of kurtosis ($kappa$) and variance ($sigma^2$) of net-proton and net-charge multiplicity distributions are carefully studied. It is shown that the statistics at RHIC/BES below $sq
rt {s_{NN}} < 19.6$ GeV are not sufficient for using the method of Centrality Bin Width Correction (CBWC). Corresponding results are systematically underestimated. A way to improve the CBWC method is proposed. It can remove the statistics dependence of the data and reduce the initial size fluctuation as well.
We report the energy and centrality dependence of dynamical kurtosis for Au + Au collisions at $sqrt{s_{NN}}$ = 7.7, 11.5, 19.6, 27, 39, 62.4 and 200 GeV at RHIC. The dynamical kurtosis of net-proton is compared to that of total-proton. The results are also compared with AMPT model calculations.
