Showing papers on "Probability-generating function published in 1974"

Bounds on the extinction time distributions of some branching processes

Abstract: The class of fractional linear generating functions, one of the few known classes of probability generating functions whose iterates can be explicitly stated, is examined. The method of bounding a probability generating function g (satisfying g ″(1) g . For the special case of the Poisson probability generating function, the best possible bounding fractional linear generating functions are obtained, and the bounds for the expected time to extinction of the corresponding Poisson branching process are better than any previously published.

A family of discrete distributions defined via their factorial moments

Abstract: This paper examines the family whose probability generating functions have the form of the generalized hypergeometric function, pFq [(a); (b); λ(s-1)] . It includes a number of matching distributions as well as many classic discrete distributions. Properties may be derived from the differential equations satisfied by the various generating functions e.g. useful recurrence formulae for probabilities, cumulants, and moments about an arbitrary point can be obtained.

Transient/steady-state solution of a single channel queue with bulk arrivals and intermittently available server

Abstract: This paper studies a single server queuing model wherein arrivals are in groups following a time homogeneous POISSON process with the group size being a random variable and the server being available intermittently. Using the LAPLACE transform and the probability generating functions, the transient and the stationary distribution of queue size are discussed and in the steady state case various means are obtained explicitly.

Computer generation of random variates

Abstract: Publisher Summary The generation of observations on random variables is based on the fact that if any random variable is operated upon by some function to produce a quantity, then a different probability distribution is obtained. If one has at his disposal a routine for generating some random variable, he might be able to generate some other random variable of interest. It is possible to generate on a computer a random variable. Another mechanism generating the negative binomial arises as a model for heterogeneity. It is assumed that the individuals of some population are randomly distributed over some region so that when the individuals in some selected area are counted, an observation from a Poisson distribution with parameter is obtained. The building block approach not only simplifies the task of generating random variables in some cases, but it can provide valuable insight into the mechanisms operating to produce a particular probability distribution as a model.