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.
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TL;DR: It is proved that for a function chosen at random from S p the order of convergence is the best possible with an arbitrarily large probability.
Abstract: Πτ-NETS give the best order of convergence of quadratures in the classes of functions Sp. It is proved that for a function chosen at random from Sp the order of convergence is the best possible with an arbitrarily large probability.
1 citations
01 Jan 1997
TL;DR: In this article, the authors show how to use computer algebra for computing exact distributions on nonparametric statistics with explicit probability generating functions, and give a new table of critical values of the Jonckheere-Terpstra test that extends tables known in the literature.
Abstract: We show how to use computer algebra for computing exact distributions on nonparametric statistics. We give several examples of nonparametric statistics with explicit probability generating functions that can be handled this way. In particular, we give a new table of critical values of the Jonckheere-Terpstra test that extends tables known in the literature.
1 citations
TL;DR: In this paper, the authors consider uniform random generation of cyclic permutations on a fixed number of symbols, which is very similar to the standard method for generating a random permutation, but is less well known.
Abstract: In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. This algorithm is very similar to the standard method for generating a random permutation, but is less well known.
We consider both methods in a unified way, and discuss their relation with exhaustive generation methods. We analyse several random variables associated with the algorithms and find their grand probability generating functions, which gives easy access to moments and limit laws.
1 citations
01 Jan 2000
TL;DR: This paper studies a discrete-time single-server queue with deterministic service times, where the server is subject to random server interruptions, and derives closed-form expressions for the probability generating functions of the buffer contents and the unfinished work.
Abstract: In this paper we study a discrete-time single-server queue with deterministic service times, where the server is subject to random server interruptions. We consider both the case where the service of a message can continue after an interruption and the case where the server has to restart the processing of the complete message after an interruption. For both alternatives, we derive closed-form expressions for the probability generating functions of the buffer contents (i.e., the number of messages in the system) and the unfinished work (i.e., the number of service time units required to empty the system). This eventually leads to explicit results for various performance measures such as the moments and the tail distribution of the system contents and the unfinished work.
1 citations
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TL;DR: In this paper, the infinite-server queueing models with homogeneous and non-homogeneous arrivals of customers and catastrophes are considered, and the probability generating functions of joint distributions of number of busy servers and served customers, as well as the Laplace-Stieltjes Transforms of distribution of busy period and distribution of cycle for the models are found.
Abstract: The infinite-server queueing models with homogeneous and non-homogeneous arrivals of customers and catastrophes are considered. The probability generating functions of joint distributions of numbers of busy servers and served customers, as well as the Laplace-Stieltjes Transforms of distribution of busy period and distribution of busy cycle for the models are found.
1 citations