  An alternative parametric description for discrete random variables, called
muculants, is proposed. In contrast to cumulants, muculants are based on the
Fourier series expansion, rather than on the Taylor series expansion, of the
logarithm of the characteristic function. We utilize results from cepstral
theory to derive elementary properties of muculants, some of which demonstrate
behavior superior to those of cumulants. For example, muculants and cumulants
are both additive. While the existence of cumulants is linked to how often the
characteristic function is differentiable, all muculants exist if the
characteristic function satisfies a Paley-Wiener condition. Moreover, the
muculant sequence and, if the random variable has finite expectation, the
reconstruction of the characteristic function from its muculants converge. We
furthermore develop a connection between muculants and cumulants and present
the muculants of selected discrete random variables. Specifically, it is shown
that the Poisson distribution is the only distribution where only the first two
muculants are nonzero.
