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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.


Papers
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Journal ArticleDOI
TL;DR: A one-dimensional lattice random walk with an absorbing boundary at the origin and a movable partial reflector is studied, suggesting a mechanism for nonuniversal kinetic critical behavior, observed in models with an infinite number of absorbing configurations.
Abstract: We study a one-dimensional lattice random walk with an absorbing boundary at the origin and a movable partial reflector. On encountering the reflector at site x, the walker is reflected (with probability r) to x-1 and the reflector is simultaneously pushed to x+1. Iteration of the transition matrix, and asymptotic analysis of the probability generating function show that the critical exponent delta governing the survival probability varies continuously between 1/2 and 1 as r varies between 0 and 1. Our study suggests a mechanism for nonuniversal kinetic critical behavior, observed in models with an infinite number of absorbing configurations.

23 citations

Journal ArticleDOI
TL;DR: In this paper, the authors give a few theorems concerning the reciprocal relation between the convergence of a sequence of distribution functions and the corresponding sequence of their moment generating functions, based on the Helly selection principle for bounded sequences of monotonic functions.
Abstract: The purpose of this paper is to give a few theorems concerning the reciprocal relation between the convergence of a sequence of distribution functions and the convergence of the corresponding sequence of their moment generating functions. The paper consists of two parts. In the first part the univariate case is discussed. The content of this part is closely related to that of a recent paper by J. H. Curtiss [1, p. 430-433], but the results are of a somewhat more general nature, and the methods of proofs are different and do not make use of the theory of a complex variable. The second part deals with the multivariate case which, as far as the author knows, has not been treated before with proofs in as complete and rigorous a way. In both the univariate and multivariate cases the proofs are based on the well known Helly selection principle [2, p. 26] for bounded sequences of monotonic functions.

23 citations

Book
01 Jan 1992
TL;DR: In this article, K.C. Kapur random processes and congestion decision trees are used to estimate probability finite sample spaces for two or more events random variable, distribution function and expected value functions of a random variable.
Abstract: Preliminaries of probability finite sample spaces two or more events random variable, distribution function and expected value functions of a random variable two or more random variables statistics quality control - control charts tolerancing, error analysis and parameter uncertainty reliability engineering, K.C. Kapur random processes and congestion decision trees. Appendices: factorial, gamma function and binomial theorem moments by Taylor Series expansion tables answers to problems.

22 citations

01 Jan 1961
TL;DR: In this article, the renewal process (process) is defined as an infinite sequence Xn X1, X2, X3, * * of independent random variables, and when all the random variables are identically distributed let us call {Xn} a renewal process.
Abstract: As a convenience, let us agree to call an infinite sequence Xn X1, X2, X3, * * of independent random variables, a renewal sequence, and when all the random variables are identically distributed let us call {Xn} a renewal process. If all the random variables are nonnegative let us say {Xn} is a positive renewal sequence (process). The renewal sequence (process) will be called periodic if there is a real w > 0 such that, with probability one, every random variable in the renewal sequence (process) is a multiple of w. If the renewal sequence (process) is not periodic we shall call it continuous. We shall write S. = Xi + X2 + Xn with n = 1, 2, 3, * , for the partial sums of the renewal sequence, Fn(x) = P{Sn _ x} for the distribution function of Sn, and U(x) = P{O _ x} for the so-called Heaviside unit function. We then define the random variable N(x) as the number of partial sums Sn which satisfy the inequality Sn _ x,

22 citations

01 Jan 2008
TL;DR: In this article, some interesting applications of Dirac's delta function in statistics have been discussed and extended to the more than one variable case while focusing on the bivariate case of the Dirac delta function.
Abstract: In this paper, we discuss some interesting applications of Dirac's delta function in Statistics We have tried to extend some of the existing results to the more than one variable case While doing that, we particularly concentrate on the bivariate case

22 citations


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