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 ...

Further, we show how some interesting properties of these probability metrics arise directly from conditions on the generating class of functions. The results are illustrated by several examples, ...

A general method is proposed for testing the fit to any member of the invariant under convolutions family of count models, parameterized by mean and variance. The test statistics, which are of the ...

Probability generating function, mean and variance of the service time distribution of an M/Gc/1 queuing model ...

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 ...

The matrices M_0, M_1 are computed using constructMatrix(g0, g1) which generates a matrix in the indicies m' by m, where each m' th row is the probability distribution for the convolution of m' copies ...

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