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: In this article, the probability generating functions of the waiting times for the first success run of length k and for the sooner run and the later run between a success run and a failure run in the second order Markov dependent trials were derived using the probability generator function method and the combinatorial method.
Abstract: The probability generating functions of the waiting times for the first success run of length k and for the sooner run and the later run between a success run of length k and a failure run of length r in the second order Markov dependent trials are derived using the probability generating function method and the combinatorial method. Further, the systems of equations of 2.m
conditional probability generating functions of the waiting times in the m-th order Markov dependent trials are given. Since the systems of equations are linear with respect to the conditional probability generating functions, they can be solved exactly, and hence the probability generating functions of the waiting time distributions are obtained. If m is large, some computer algebra systems are available to solve the linear systems of equations.
51 citations
01 Jan 1974
50 citations
TL;DR: Some techmques for solving recurrences are presented, along with examples of how these Recurrences arise in the analysis of algorithms.
Abstract: Some techmques for solving recurrences are presented, along with examples of how these recurrences arise in the analysis of algorithms. In addition, probability generating functions are discussed and used to analyze problems in computer science.
50 citations
TL;DR: In this article, a Gaussian distributed random variable is used to model the relationship between magnitude estimates and signals intensity, and a linear response function is used for the counting model with a constant sample size counting model.
50 citations
TL;DR: In this article, the authors derived a Lundberg type result for asymptotic ruin probabilities in the case of a risk process with dependent increments, assuming that the probability generating functions exist, and that their logarithmic average converges.
Abstract: In this paper, we derive a Lundberg type result for asymptotic ruin probabilities in the case of a risk process with dependent increments We only assume that the probability generating functions exist, and that their logarithmic average converges Under these assumptions we present an elementary proof of the Lundberg limiting result, which only uses simple exponential inequalities, and does not rely on results from large deviation theory Moreover, we use dependence orderings to investigate, how dependencies between the claims affect the Lundberg coefficient The results are illustrated by several examples, including Gaussian and AR(1)-processes, and a risk process with adapted premium rules
48 citations