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: A comprehensive survey of the different methods of generating discrete probability distributions as analogues of continuous probability distributions is presented along with their applications in construction of new discrete distributions.
Abstract: In this paper a comprehensive survey of the different methods of generating discrete probability distributions as analogues of continuous probability distributions is presented along with their applications in construction of new discrete distributions. The methods are classified based on different criterion of discretization.
105 citations
TL;DR: In this article, an expression for the cumulant generating function of the multi-dimensional response of a linear system to Poisson distributed random impulses is obtained, which enables estimates to be made of the joint probability distribution of the response, when the latter is slightly non-Gaussian.
98 citations
TL;DR: In this article, a method for the evaluation of the stationary and non-stationary probability density function of non-linear oscillators subjected to random input is presented, which requires the approximation of the probability density functions of the response in terms of C-type Gram-Charlier series expansion.
Abstract: A method for the evaluation of the stationary and non-stationary probability density function of non-linear oscillators subjected to random input is presented. The method requires the approximation of the probability density function of the response in terms of C-type Gram-Charlier series expansion. By applying the weighted residual method, the Fokker-Planck equation is reduced to a system of non-linear first order ordinary differential equations, where the unknowns are the coefficients of the series expansion. Furthermore, the relationships between the A-type and C-type Gram-Charlier series coefficient are derived.
86 citations
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01 Jun 196584 citations
12 Jul 2011
TL;DR: To the runtime analysis of evolutionary algorithms two powerful techniques are introduced: probability-generating functions and variable drift analysis, which are shown to provide a clean framework for proving sharp upper and lower bounds.
Abstract: We introduce to the runtime analysis of evolutionary algorithms two powerful techniques: probability-generating functions and variable drift analysis. They are shown to provide a clean framework for proving sharp upper and lower bounds. As an application, we improve the results by Doerr et al. (GECCO~2010) in several respects. First, the upper bound on the expected running time of the most successful quasirandom evolutionary algorithm for the OneMax function is improved from 1.28n ln n to 0.982n ln n, which breaks the barrier of n ln n posed by coupon-collector processes. Compared to the classical 1+1-EA, whose runtime will for the first time be analyzed with respect to terms of lower order, this represents a speedup by more than a factor of e=2.71...
74 citations