Abstract
An alternative parametric description for discrete random variables, called
muculants, is proposed. Contrary to cumulants, muculants are based on the
Fourier series expansion rather than on the Taylor series expansion of the
logarithm of the characteristic function. Utilizing results from cepstral
theory, elementary properties of muculants are derived. A connection between
muculants and cumulants is developed, and the muculants of selected discrete
random variables are presented. Specifically, it is shown that the Poisson
distribution is the only discrete distribution where only the first two
muculants are non-zero, thus being the muculant-counterpart of the simple
cumulant structure of Gaussian distributions.
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