As   we all know, the precise measurement of higher moments requires very   high statistics. Although relativistic heavy ion collisions already  have  very high statistics, are they sufficiently accurate to measure  higher  moments (especially the 4th and 6th moments)? What is the relationship between statistics and measurement accuracy? There is no basis for this. Based on our accumulated work on RHIC/BES I high-order moment measurements, we conducted a systematic study of this issue.
We   first use the UrQMD transport model to give the dependence of the   product (κσ2) of the net proton and static charge's fourth moment and   variance on the statistic. When   the RHIC energy is lower than 19.6 GeV, the existing event statistics   of the experiment are insufficient to analyze the fourth-order moments   using the central width correction method (CBWC). It will cause the corresponding calculation result system to be depressed. We propose an improved CBWC method. Under the existing RHIC statistics, it can eliminate the dependence of the fourth moment on the statistics. Moreover, the influence of the fourth moment on the initial volume fluctuation can be effectively reduced. This work was published in J. Phys. G: Nucl. Part. Phys. 41, 105107 (2014). It was agreed by two reviewers.
Next,   based on a simple simulation, we studied the dependence of the mean  and  probability distributions of the measured higher moments on the   statistics, and estimated the statistics required for all the higher   order moments of interest and their products. Why the measured values are underestimated when statistics are insufficient. In   the case of existing RHIC/BES I statistics, the 2nd and 3rd order   moments can be reliably measured by the central width correction method   (CBWC). However, reliable fourth-order moment measurements cannot be obtained in this way in low energy regions. In   the future RHIC/BES II statistics, using the improved CBWC method is   expected to obtain a reliable fourth-order moment measurement result. This work was published in J. Phys. G: Nucl. Part. Phys. 42, 065103 (2015).
These   conclusions are of great significance for us to correctly understand   the dependence of the conserved Dutch high order moments on the   collision energy and the centrality observed in the current experiment,   and to provide important guidance for the experimental measurement of   higher moments on the RHIC/BES II in the future.