Showing papers on "Probability-generating function published in 1983"
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: The technique is particularily useful for generating experimental stimuli for system identification, sequences for numerical simulation, and test series for evaluating signal processing algorithms when colored (non-white) non-Gaussian data are required.
Abstract: A new method is presented for the generation of stochastic (random) sequences with an arbitrarily specified first-order probability distribution function (PDF) and an arbitrarily specified first-roder auto-correlation function (ACF). A set of numbers with the desired PDF are first generated. These are then given a white (independent) ACF by double stochastic interchange. The desired ACF is then obtained by stochastically shuffling the series to minimize a sum of squares criterion between desired and actual ACFs. The technique is particularily useful for generating experimental stimuli for system identification, sequences for numerical simulation, and test series for evaluating signal processing algorithms when colored (non-white) non-Gaussian data are required.
46 citations
TL;DR: A discrete-time buffer system with one randomly interrupted output channel is considered and it is shown how relationships can be found between the probability generating functions of the buffer occupancy at various time instants.
Abstract: A discrete-time buffer system with one randomly interrupted output channel is considered. It is shown how relationships can be found between the probability generating functions of the buffer occupancy (expressed in number of messages) at various time instants. The use of these relationships is illustrated.
30 citations
TL;DR: This paper considers the service system MX/G/∞ characterized by an infinite number of servers and a general service time distribution, which is a random variable, the time between group arrivals being exponentially distributed.
25 citations
TL;DR: In this paper, the first hitting times in random walks (skip-free Markov chains on the non-negative integers) are studied and their probability generating functions are expressed in terms of the eigenvalues of probability transition submatrices.
Abstract: Distributions for first hitting times in random walks (skip-free Markov chains on the non-negative integers) are studied. Their probability generating functions are expressed in terms of the eigenvalues of probability transition submatrices. The study of first hitting times leads to several classes of infinitely divisible distributions closely related to the Bondesson class of generalized convolutions of mixtures of exponential distributions which arises from the study of first hitting times in birth-death processes. Some properties of these classes are derived from their characterization by Pick functions.
14 citations
TL;DR: In this article, a response function method using externally applied random force is developed to identify linear or nonlinear systems using the probability distribution function of fluctuations and probability flow in phase space.
Abstract: A response function method using externally applied random force is developed to identify linear or nonlinear systems. The probability distribution function of fluctuations and probability flow in phase space are used as the means for these identifications. It is also demonstrated that anomalous behavior of these quantities can be utilized as the forerunner phenomenon of the catastrophe of unstable systems.
2 citations
TL;DR: In this paper, a simple proof is given to show that there always exists a neighborhood of zero in which a moment generating function has a power series expansion, and the relation between moments and derivatives of the moment generator at zero can be obtained without resorting to postcalculus theorems.
Abstract: A simple proof is given to show that there always exists a neighborhood of zero in which a moment generating function has a power series expansion. Thus, the relation between moments and derivatives of the moment generating function at zero can be obtained without resorting to postcalculus theorems.
1 citations
1 citations
TL;DR: In this paper, an expression for the generating functional of a statistical system suitable for describing two-phase states of matter was derived starting from an assumed form of the distribution function near the phase transition point.
Abstract: Starting from an assumed form of the distribution function near the phase transition point, an expression for the generating functional of a statistical system suitable for describing two-phase states of matter is derived We then obtain formulas for the partition function and correlation functions by the standard procedure
TL;DR: In this paper, a general procedure to calculate the probability density function of a function of random variable is presented, which has been successfully used at the undergraduate level for several semesters at the Pontificia Universidade Catolica do Rio de Janeiro.
Abstract: A general procedure to calculate the probability density function of a function of a random variable is presented. Although it is not really a new method of solving this problem, it is a procedure which is organized and developed in a manner better suited to student understanding and application than other methods. This technique has been successfully used at the undergraduate level for several semesters at the Pontificia Universidade Catolica do Rio de Janeiro.