In continuation of our earlier work, in which we analysed the charged particle multiplicities in leptonic and hadronic interactions at different center-of-mass energies in full phase space as well as in restricted phase space using the shifted Gompertz distribution, a detailed analysis of the normalized moments and normalized factorial moments is reported here. A two-component model in which a probability distribution function is obtained from the superposition of two shifted Gompertz distributions, as introduced in our earlier work, has also been used for the analysis. This is the first analysis of the moments with the shifted Gompertz distribution. Analysis has also been performed to predict the moments of multiplicity distribution for the e + e − collisions at s = 500 GeV at a future collider.