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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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TL;DR: The moments of a Catalan triangle are computed using a combinatorial approach similar to that used for probability generating functions, such as Eulerian numbers, runs, zig-zag permutations, tangent numbers and a kind of nontrivial run called a slide as discussed by the authors.
Abstract: The moments of a Catalan triangle are computed. The method is similar to that used for probability generating functions. This however does not explain the elegance of the results until further combinatorial connections are developed. These include Eulerian numbers, runs, zig-zag permutations, tangent numbers and a kind of nontrivial run called a slide.
73 citations
TL;DR: This article presented new characterizations of the integer-valued moving average model and gave moments and probability generating functions for four model variants, including Yule-Walker and conditional least-order.
Abstract: The paper presents new characterizations of the integer-valued moving average model. For four model variants, we give moments and probability generating functions. Yule-Walker and conditional least ...
70 citations
TL;DR: This paper presents a meta-analyses of the derivation of mertn time to loss of track for B certain AFC system in the presence of two fluctuating targets by E. Baghdady and M. Buchner, Jr.
Abstract: REFERENCES [l] E. J. Baghdady, Lectures on Communication System Theory. New York: McGraw-Hill, ch. 19, sec. 5.3. [2] M. M. Buchner, Jr., “Derivation of mertn time to loss of track for B certain AFC system in the presence of two fluctuating targets,” The Johns Hopkins University. Brtltimore, Md., Applied Physics Lab. memo BSA-1-038, August 14. 1964 (memo clmmfied &8 confidential, title unclassified). [3] S. 0. Rice, “Distribution of the duration of fades in radio transmission,” Bell Sys. Tech. J., vol. 37. pp. 581-635. May 1958. [4] -, “Mathematical amlysis of random noise,” Bell Sys. Tech. J.. vol. 24, pp. 46-156. January 1945. [5] D. Middleton. “Spurious signals caused by noise in triggered circuits,” J. Appl. Phys., vol. 19, pp. 817-830, September 1948.
69 citations
TL;DR: In this paper, a method for analyzing flow through a porous medium whose parameters are random functions is presented, which is similar to the Galerkin formulation except the coefficients in the linear combination are no longer deterministic quantities but random functions.
Abstract: A method is presented for analyzing flow through a porous medium whose parameters are random functions. Such a medium is conceptualized as an ensemble of media with an associated probability mass function. The flow problem in each member of this ensemble is deterministic in the usual sense. All the solutions belong to a particular Hilbert space, and hence they can be written in terms of linear combinations of its basis functions. This is similar to the Galerkin formulation except that the coefficients in the linear combination are no longer deterministic quantities but random functions. The finite element method in conjunction with a Taylor series expansion is used to get the first two moments of the solution approximately. The method does not require specification of full probability mass functions of the parameters but only their first two moments, and spatial correlations can be easily accounted for. However, it is assumed that the probability mass functions are peaked at the expected value and are smooth in its vicinity. A sample problem is solved to illustrate the procedure. It is observed that the result is sensitive to the element size in the numerical scheme and the variances and spatial correlations of parameters. The expected value of the hydraulic head is found to differ significantly from the results that would have been obtained if the problem had been solved deterministically.
66 citations
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01 Jan 1998TL;DR: In this paper, the authors presented new characterizations of the integer-valued moving average model for four model variants and gave moments and probability generating functions for each model variant and showed that the small sample performance is in some instances better than those of alternative estimators.
Abstract: The paper presents new characterizations of the integer-valued moving average model. For four model variants we give moments and probability generating functions. Yule-Walker and conditional least squares estimators are obtained and studied by Monte Carlo simulation. A new generalized method of moment estimator based on probability generating functions is presented and shown to be consistent and asymptotically normal.The small sample performance is in some instances better than those of alternative estimators. The techniques are illustrated on a time series of traded stocks.
65 citations