Topic
Probability-generating function
About: Probability-generating function is a research topic. Over the lifetime, 752 publications have been published within this topic receiving 9361 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, the authors introduce the concepts of discrete semi-stability and geometric semisuperstability for distributions with support in Z+ and offer several properties, including characterizations, of such distributions.
Abstract: The purpose of this paper is to introduce and study the concepts of discrete semi-stability and geometric semi-stability for distributions with support inZ+. We offer several properties, including characterizations, of discrete semi-stable distributions. We establish that these distributions posses the property of infinite divisibility and that their probability generating functions admit canonical representations that are analogous to those of their continuous counterparts. Properties of discrete geometric semi-stable distributions are deduced from the results obtained for discrete semi-stability. Several limit theorems are established and some examples are constructed.
17 citations
TL;DR: In this paper, a multitype Galton-Watson process is used to model a bird population and it is shown that such behaviour can correspond to maximization of the probability of survival of the species to time t for each finite t.
Abstract: Many species of birds have a characteristic clutch size which is either fixed at k or is of the form k or k + 1 for some appropriate integer k. In this paper we show, using a multitype Galton-Watson process to model a bird population, that such behaviour can correspond to maximization of the probability of survival of the species to time t for each finite t. This is also a conclusion which might be drawn from the theory of natural selection and hence provides some mathematical evidence of the force of evolution. The results of the paper rest on a bounding of probability generating functions.
17 citations
TL;DR: The mathematical model is constructed and the probability generating functions of number of customers in the system when it is idle, busy, on vacation and under repair are derived.
Abstract: This paper investigates the steady state behaviour of an M[x]/G/1 retrial queue with two phases of service under Bernoulli vacation schedule and breakdown. Any arriving batch finding the server busy, breakdown or on vacation enters an orbit. Otherwise one customer from the arriving batch enters the service immediately while the rest join the orbit. After completion of each two phases of service, the server either goes for a vacation with probability p or may wait for serving the next customer with probability (1-p). While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. We construct the mathematical model and derive the probability generating functions of number of customers in the system when it is idle, busy, on vacation and under repair. Some system performances are obtained.
17 citations
TL;DR: Universal generators for absolutely-continuous and integer-valued random variables are introduced, based on a generalization of the rejection technique proposed by Devroye, which gives rise to simple algorithms which may be implemented in a few code lines and may show noticeable performance even if some classical families of distributions are considered.
Abstract: Universal generators for absolutely-continuous and integer-valued random variables are introduced. The proposal is based on a generalization of the rejection technique proposed by Devroye [The computer generation of random variables with a given characteristic function. Computers and Mathematics with Applications. 1981;7:547–552]. The method involves a dominating function solely requiring the evaluation of integrals which depend on the characteristic function of the underlying random variable. The proposal gives rise to simple algorithms which may be implemented in a few code lines and which may show noticeable performance even if some classical families of distributions are considered.
17 citations
TL;DR: In this paper, the properties of a random process consisting of the sum of a series of sine waves with deterministic amplitudes and independent, random phase angles were analyzed. But the analysis was restricted to a single sine wave and the probability density of the series, its peaks and envelope have been found for an arbitrary number of sines in the series.
16 citations