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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.


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Journal ArticleDOI
Muniru A. Asiru1
TL;DR: In this paper, the expected number of observations is obtained using the method of geometric transforms (probability generating functions) until the sequence pattern 123, N, N and N, which is an outcome in a sequence of independent multinomial observations.
Abstract: The expected value (mean) is one of the most important measures of central tendency used both in statistics and in the mathematical theory of probability. Using the method of geometric transforms (probability generating functions), the expected number of observations is obtained until the sequence pattern 123…N123…N…123…N, which is an outcome in a sequence of independent multinomial observations. The results and the flow graph analysis obtained agree with and provide the generalization of similar problems considered earlier in this journal.
01 Jan 1972
TL;DR: In this article, the higher-order transition probability generating functions for a random walk with correlation between steps are calculated as a discrete-domain Green's function, which is the same as the one used in this paper.
Abstract: The higher-order transition probability generating functions for a randomwalk with correlation between steps is calculated as a discrete-domain Green's function.
Journal Article
TL;DR: A single server retrial queuing system with two stages heterogeneous service with time dependent probability generating functions in terms of their Laplace transforms and the corresponding steady state results explicitly is investigated.
Abstract: T his paper investigates a single server retrial queuing system with two stages heterogeneous serviceCustomers arrive in batches in accordance with compound Poisson processes After the completion of first stage service, the second stage service starts with probability 1 In addition to this, the server takes Bernoulli vacation and setup times We assume that the retrial time, the service time, the repair time, the vacation time and the setup time of the server are all arbitrarily distributed We obtain the time dependent probability generating functions in terms of their Laplace transforms and the corresponding steady state results explicitly Also we derive the average number of customers in the queue and the average waiting time in closed form with numerical illustration
Journal ArticleDOI
Kiyoshi Inoue1
TL;DR: In this article, the authors considered random occupancy models and the related problems based on the methods of generating functions and provided the effective computational tools for the evaluation of the probability functions by making use of the Bell polynomials.
Abstract: In this article, we consider random occupancy models and the related problems based on the methods of generating functions. The waiting time distributions associated with sequential random occupancy models are investigated through the probability generating functions. We provide the effective computational tools for the evaluation of the probability functions by making use of the Bell polynomials. The results presented here provide a wide framework for developing the theory of occupancy models. Finally, we treat several examples in order to demonstrate how our theoretical results are employed for the investigation of the random occupancy models along with numerical results.

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20236
202211
20217
202014
201912
20188