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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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Journal ArticleDOI
TL;DR: In this paper, the stochastic foundations for ultra-low diffusion were developed based on random walks with a random waiting time between jumps whose probability tail falls off at a logarithmic rate.

132 citations

Journal ArticleDOI
TL;DR: In this paper, the surface elevation probability density function and associated statistical properties for a wind-generated wave field were compared with the results derived from the Longuet-Higgins (1963) theory.
Abstract: Laboratory experiments were performed to measure the surface elevation probability density function and associated statistical properties for a wind-generated wave field. The laboratory data along with some limited field data were compared. The statistical properties of the surface elevation were processed for comparison with the results derived from the Longuet-Higgins (1963) theory. It is found that, even for the highly non-Gaussian cases, the distribution function proposed by Longuet-Higgins still gives good approximations.

132 citations

Journal ArticleDOI
TL;DR: In this article, a theoretical method for predicting the longitudinal dispersion coefficient is developed based on the transverse velocity distribution in natural streams, which is the most appropriate model for explaining the complex behavior of the transversal velocity structure of irregular natural streams.
Abstract: In this study, a theoretical method for predicting the longitudinal dispersion coefficient is developed based on the transverse velocity distribution in natural streams. Equations of the transverse velocity profile for irregular cross sections of the natural streams are analyzed. Among the velocity profile equations tested in this study, the beta distribution equation, which is a probability density function, is considered to be the most appropriate model for explaining the complex behavior of the transverse velocity structure of irregular natural streams. The new equation for the longitudinal dispersion coefficient that is based on the beta function for the transverse velocity profile is developed. A comparison of the proposed equation with existing equations and the observed longitudinal dispersion coefficient reveals that the proposed equation shows better agreement with the observed data compared to other existing equations.

132 citations

Journal ArticleDOI
TL;DR: An efficient approach for the evaluation of the Nakagami-m (1960) multivariate probability density function (PDF) and cumulative distribution function (CDF) with arbitrary correlation is presented and useful closed formulas are derived.
Abstract: An efficient approach for the evaluation of the Nakagami-m (1960) multivariate probability density function (PDF) and cumulative distribution function (CDF) with arbitrary correlation is presented. Approximating the correlation matrix with a Green's matrix, useful closed formulas for the joint Nakagami-m PDF and CDF, are derived. The proposed approach is a significant theoretical tool that can be efficiently used in the performance analysis of wireless communications systems operating over correlative Nakagami-m fading channels.

132 citations

Journal ArticleDOI
TL;DR: In this paper, a statistically equivalent periodic unit cell (SEPUC) is constructed such that its morphology conforms with images of real microstructures such as a fiber tow, a plain weave textile composite and an irregular-coursed masonry wall.
Abstract: A unified treatment of random microstructures proposed in this contribution opens the way to efficient solutions of large-scale real world problems. The paper introduces a notion of statistically equivalent periodic unit cell (SEPUC) that replaces in a computational step the actual complex geometries on an arbitrary scale. A SEPUC is constructed such that its morphology conforms with images of real microstructures. Here, the appreciated two-point probability function and the lineal path function are employed to classify, from the statistical point of view, the geometrical arrangement of various material systems. Examples of statistically equivalent unit cells constructed for a unidirectional fibre tow, a plain weave textile composite and an irregular-coursed masonry wall are given. A specific result promoting the applicability of the SEPUC as a tool for the derivation of homogenized effective properties that are subsequently used in an independent macroscopic analysis is also presented.

131 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023382
2022906
2021906
20201,047
20191,117
20181,083