The evolution of multiplicity distribution of a species which undergoes chemical reactions can be described with the help of a master equation. We study the master equation for a fixed temperature, because we want to know how fast different moments of the multiplicity distribution approach their equilibrium value. We particularly look at the 3rd and 4th factorial moments and their equilibrium values from which central moments, cumulants and their ratios can be calculated. Then we study the situation in which the temperature of the system decreases. We find out that in the non-equilibrium state, higher factorial moments differ more from their equilibrium values than the lower moments and that the behaviour of the combination of the central moments depends on the combination we choose. If one chooses to determine the chemical freeze-out temperature from the measured values of higher moments, these effects might jeopardise the correctness of the extracted value.