Showing papers on "Probability-generating function published in 1982"
TL;DR: In this paper, analogues of the concept of self-decomposability are proposed for distributions on the set ℕ 0 of nonnegative integers, which correspond to an analogue of multiplication (in distribution) that preserves Ω0-valuedness and is characterized by a composition semigroup of probability generating functions, such as occur in branching processes.
Abstract: Self-decomposable distributions are known to be absolutely continuous. In this note analogues of the concept of self-decomposability are proposed for distributions on the set ℕ0 of nonnegative integers. To each of them corresponds an analogue of multiplication (in distribution) that preserves ℕ0-valuedness and is characterized by a composition semigroup of probability generating functions, such as occur in branching processes.
39 citations
TL;DR: In this article, the authors considered the problem of random graphs as a bond percolation problem and derived a closed form expression for the cluster-size generating function from which the mean cluster size as well as the per-colation probability were derived.
Abstract: The problem of random graphs, which arises in the analysis of network reliability in communication theory, is considered here as a bond percolation. A closed form expression is obtained for the cluster-size generating function from which the mean cluster size as well as the percolation probability are derived. In a network of N to infinity stations in which the communication between any two stations is intact with a probability alpha /N, it is found that for alpha 1 there is a non-zero percolation probability.
12 citations
TL;DR: In this paper, power series techniques for differential equations on probability generating functions are applied to derive recursive formulas for discrete compound distributions, which are computationally effective and useful in risk theory.
Abstract: We apply power series techniques for differential equations on probability generating functions to derive recursive formulas for discrete compound distributions. Such formulas are computationally effective and useful in risk theory.
10 citations
01 Jun 1982
TL;DR: In this article, the probability distribution of the waiting times associated with specified events, and how they generalize the Fibonacci, Tribonacci and..., sequences in different ways are considered.
Abstract: Suppose we have a multinormal population with k possible outcomes E/sub 1/, E/sub 2/, ..., E/sub k/ and associated probabilities ..pi../sub 1/, ..pi../sub 2/, ..., ..pi../sub k/. At each of the independent trials, one of the outcomes is observed. One may be interested in the waiting time for the occurrence of a specified event, which consists of a succession of outcomes. In this paper, we consider the probability distribution of the waiting times associated with specified events, and show how they generalize the Fibonacci, Tribonacci, ..., sequences in different ways. This is possible, since the probability generating functions of the associated waiting time random variables can be utilized to derive the probability distributions.
9 citations
TL;DR: Probability generating functions evaluated on finite difference operators were used systematically to derive formulas for moments of discrete distributions in this article, where they were used to derive probability generating functions for moments in discrete distributions.
Abstract: Probability generating functions evaluated on finite difference operators are used systematically to derive formulas for moments of discrete distributions.
5 citations
TL;DR: In this article, a general method of obtaining the probability generating function (pgf) of a Modified Power Series distribution (MPSD), introduced by GUPTA (1974), is presented.
Abstract: In this paper, a general method of obtaining the probability generating function (pgf) of a Modified Power Series distribution (MPSD), introduced by GUPTA (1974), is presented. This method is employed to derive the pgf of generalized negative binomial, generalized Poisson, generalized logarithmic series and the lost game distribution.
3 citations