Generalizing Phi-measure of event-by-event fluctuations in high-energy heavy-ion collisions

The Phi-measure of event-by-event fluctuations in high-energy heavy-ion collisions corresponds to the second moment of the fluctuating quantity distribution of interest. It is shown that the measure based on the third moment preserves the properties of Phi but those related to the higher moments do not. In particular, only the second and third moment measures are intensive as thermodynamic quantities. The Phi_2- and Phi_3-measure of p_T-fluctuations are computed for the hadron gas in equilibrium and the results are analyzed in context of the experimental data.