The probability generating function is the most important mathematical technique to examine the transient and steady state behavior of queueing models, particularly to explore many significant ...

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 ...

In this paper, our central attention is to explore the probability generating functions using Rouche’s theorem in both cases of slower and faster arrival rates of the queueing model taken into ...

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 ...

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 ...

For scaled random matrices with orthogonal symmetry, and the interval at the hard or soft spectrum edge, the gap probability generating functions have the special property that they can be evaluated ...

The classic probability data association filter is derived using generating functions. It is shown that there is a one-to-one correspondence between the terms of the cross-derivative of the generating ...

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 ...

A probability density function (PDF) describes the likelihood of different outcomes for a continuous random variable.