  Fluctuations of conserved quantities are predicted to be sensitive to the
correlation length and connected to the thermodynamic susceptibility. Thus,
moments of net-baryon, net-charge and net-strangeness have been extensively
studied theoretically and experimentally to explore phase structure and bulk
properties of QCD matters created in heavy ion collision experiment. As the
moments analysis is statistics hungry study, the error estimation is crucial to
extract physics information from the limited experimental data. In this paper,
we will derive the limit distributions and error formula based on Delta theorem
in statistics for various order moments used in the experimental data analysis.
The Monte Carlo simulation is also applied to test the error formula.
