Topic
Probability density function
About: Probability density function is a research topic. Over the lifetime, 22321 publications have been published within this topic receiving 422885 citations. The topic is also known as: probability function & PDF.
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TL;DR: The authors extend multicanonical sampling to the determination of probability density functions in communications systems and generate the probability of both frequent and rare events with equivalent accuracy through an easily programmed iterative procedure.
Abstract: The authors extend multicanonical sampling to the determination of probability density functions in communications systems. The resulting easily programmed iterative procedure generates the probability of both frequent and rare events with equivalent accuracy. The applicability of the technique is verified through a calculation of the differential group delay probability distribution in a multisection polarization emulator.
95 citations
TL;DR: In this article, the authors describe a procedure for the robust design of water distribution networks which incorporates the uncertainty of nodal water demands and pipe roughness in a multiobjective optimization scheme aimed at minimizing costs and maximizing hydraulic reliability.
Abstract: The paper describes a procedure for the robust design of water distribution networks which incorporates the uncertainty of nodal water demands and pipe roughness in a multiobjective optimization scheme aimed at minimizing costs and maximizing hydraulic reliability. The methodology begins with a deterministic system design in order to generate a set of optimal networks that serves as the initial population for subsequent multiobjective stochastic design. This approach does not depend on the choice of multiobjective optimizer (for example, a multiobjective genetic algorithm is used here) and can drastically reduce the number of “stochastic” runs needed for searching robust solutions. A collection of probability density functions based on the β function is introduced and applied to modeling variable uncertainty according to different physical requirements. The approach is tested in a case study involving a real network, illustrating its computational advantages.
95 citations
TL;DR: In this paper, the Weibull three-parameter model is discussed for estimation of mean wind power densities and the variation with height of the three parameters of the discussed model is investigated; no simple height dependence can be proposed.
Abstract: The Weibull three-parameter model is discussed for estimation of mean wind power densities. This probability density function is a generalization of a number of more conventional density functions. Using wind speed observations, it is shown that this model generally gives a more reliable fit to the empirical wind speed frequency data than the density functions with one or two parameters. Wind power density estimations turn out to be strongly dependent on the hypothesized probability density function. The variation with height of the three parameters of the discussed model is investigated; no simple height dependence can be proposed.
95 citations
TL;DR: A minimally subjective approach for uncertainty quantification in data-sparse situations, based on a new and purely data-driven version of polynomial chaos expansion (PCE), achieves a significant computational speed-up compared with Monte Carlo as well as high accuracy even for small orders of expansion, and shows how this novel approach helps overcome subjectivity.
94 citations
IBM1
TL;DR: The deep learning model DE-LSTM, which aims to approximate the probability density function of a stochastic process via numerical discretization and the underlying nonlinear dynamics is modeled by the Long Short-Term Memory network, makes a good prediction of the probability distribution without assuming any distributional properties of the stochastics process.
94 citations