Probability generating functions are often employed for their succinct description of the sequence of probabilities $\Pr (X = i)$ in the probability mass function for a random variable X, and to make ...

A numerical method is presented for calculating the cumulative distribution of a positive random variable from its moment-generating function. It involves an expansion of the rectangular function in ...

Discover the power of Generalized Method of Moments (GMM) based on probability generating function. Unify estimation and model testing, while enjoying distribution-free chi-square tests. Overcome ...

Generalized method of moments based on probability generating function is considered. Estimation and model testing are unified using this approach which also leads to distribution free chi-square ...

The results of this paper deal directly with the behavior of compositions of random probability generating functions. These results are then applied to the theory of branching processes with random ...

Any ARUM can be characterized by a choice-probability generating function (CPGF) whose gradient gives the choice probabilities, and every CPGF is consistent with an ARUM. We relate CPGF to ...

Leo A. Aroian, The Probability Function of the Product of Two Normally Distributed Variables, The Annals of Mathematical Statistics, Vol. 18, No. 2 (Jun., 1947), pp. 265-271 ...

Generating function techniques have been extensively used to analyze the performance of both convolutional and trellis codes over AWGN and Rayleigh fading chann ...

For simplicity, we considered networks consisting of two-body catalytic reactions. We used the probability generating function method to obtain the steady-state solutions of the chemical master ...