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.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, a new data assimilation approach based on the particle filter (PF) was proposed for nonlinear/non-Gaussian applications in geoscience, denoted the local PF, which extends the particle weights into vector quantities to reduce the influence of distant observations on the weight calculations via a localization function.
Abstract: This paper presents a new data assimilation approach based on the particle filter (PF) that has potential for nonlinear/non-Gaussian applications in geoscience. Particle filters provide a Monte Carlo approximation of a system’s probability density, while making no assumptions regarding the underlying error distribution. The proposed method is similar to the PF in that particles—also referred to as ensemble members—are weighted based on the likelihood of observations in order to approximate posterior probabilities of the system state. The new approach, denoted the local PF, extends the particle weights into vector quantities to reduce the influence of distant observations on the weight calculations via a localization function. While the number of particles required for standard PFs scales exponentially with the dimension of the system, the local PF provides accurate results using relatively few particles. In sensitivity experiments performed with a 40-variable dynamical system, the local PF require...
159 citations
TL;DR: In this paper, the mean area of isoconcentration surface per unit volume is studied through its transport equation derived by using the probability density function (pdf) formalism, which allows the value of the reactive scalar used to define the level surface to be treated as an independent variable.
Abstract: To characterize the dynamics and the physical properties of isoconcentration surfaces of a random reactive scalar field, an instantaneous isosurface quantity and its transport equation are introduced. For turbulent flows, the mean area of isoconcentration surface per unit volume is studied through its transport equation derived by using the probability density function (pdf) formalism. This approach allows the value of the reactive scalar used to define the level surface to be treated as an independent variable. It also leads to the definition of a surface density function. The developed formalism is applied to premixed turbulent combustion and a bridge is built between modeling approaches based on pdf, and others based on the flame surface concept.
159 citations
TL;DR: In this paper, the authors consider the application of Bernstein polynomials for approximating a bounded and continuous function and show that it can be naturally adapted for smooth estimation of a distribution function concentrated on the interval [0, 1] by a continuous approximation of the empirical distribution function.
159 citations
TL;DR: The instanton solution for the forced Burgers equation is found that describes the exponential tail of the probability distribution function of velocity differences in the region where shock waves are absent; that is, for large positive velocity differences.
Abstract: The instanton solution for the forced Burgers equation is found. This solution describes the exponential tail of the probability distribution function of velocity differences in the region where shock waves are absent; that is, for large positive velocity differences. The results agree with the one found recently by Polyakov, who used the operator product conjecture. If this conjecture is true, then our WKB asymptotics of the Wyld functional integral should be exact to all orders of perturbation expansion around the instanton solution. We also generalized our solution for the arbitrary dimension of the Burgers (KPZ) equation. As a result we found the asymptotics of the angular dependence of the velocity difference probability distribution function. \textcopyright{} 1996 The American Physical Society.
158 citations
TL;DR: This work studies numerically rogue waves in dissipative systems, taking as an example a unidirectional fiber laser in a nonstationary regime of operation and finding that the probability of producing extreme pulses in this setup is higher than in any other system considered so far.
Abstract: We study numerically rogue waves in dissipative systems, taking as an example a unidirectional fiber laser in a nonstationary regime of operation. The choice of specific set of parameters allows the laser to generate a chaotic sequence of pulses with a random distribution of peak amplitudes. The probability density function for the intensity maxima has an elevated tail at higher intensities. We have found that the probability of producing extreme pulses in this setup is higher than in any other system considered so far.
158 citations