Fourth-order cumulants of physical quantities have been used to characterize the nature of a phase transition. In this paper we report some Monte Carlo simulations to illustrate the behavior of fourth-order cumulants of magnetization and energy across second and first-order transitions in the phase diagram of a well know spin-1 Ising model. Simple ideas from the theory of thermodynamic fluctuations are used to account for the behavior of these cumulants.
