Related papers: Closed Form Expressions for the Probability Densit…
Intermittency in MHD turbulence has been analyzed using high resolution 2D numerical simulations. We show that the Probability Distribution Functions (PDFs) of the fluctuations of the Elsasser fields, magnetic field and velocity field…
The probability distribution function (PDF) of the mass surface density is an essential characteristic of the structure of molecular clouds or the interstellar medium in general. Observations of the PDF of molecular clouds indicate a…
We report a first study of time-dependent Probability Density Functions (PDFs) in the Low-to- High confinement mode (L-H) transition by extending the previous prey-predator-type model (Kim & Diamond, Phys. Rev. Lett. 91, 185006, 2003) to a…
Employing molecular dynamics simulations of jammed soft particles, we study microscopic responses of force-chain networks to quasi-static isotropic (de)compressions. We show that not only contacts but also interparticle gaps between the…
Very often, in the course of uncertainty quantification tasks or data analysis, one has to deal with high-dimensional random variables (RVs). A high-dimensional RV can be described by its probability density (pdf) and/or by the…
Under ideal conditions, the probability density function (PDF) of a random variable, such as a sensor measurement, would be well known and amenable to computation and communication tasks. However, this is often not the case, so the user…
Distance distributions are a key building block in stochastic geometry modelling of wireless networks and in many other fields in mathematics and science. In this paper, we propose a novel framework for analytically computing the closed…
The statistics of power fluctuations are studied in simulations of two-dimensional turbulence in both inverse (energy) and direct (enstrophy) cascade regimes from both Lagrangian and Eulerian perspectives. The probability density function…
We present a numerical approach for estimating the probability density function (PDF) of quantities of interest (QoIs) of power grid systems subject to uncertain power generation and load fluctuations. In our approach, generation and load…
In this work, the product of two independent and non-identically distributed (i.n.i.d) $\kappa - \mu $ shadowed random variables is studied. We derive the series expression for the probability density function (PDF), cumulative distribution…
We consider the tails of probability density function (PDF) for the velocity that satisfies Burgers equation driven by a Gaussian large-scale force. The saddle-point approximation is employed in the path integral so that the calculation of…
Power-law probability density function (PDF) plays a key role in both subdiffusion and L\'{e}vy flights. However, sometimes because of the finite of the lifespan of the particles or the boundedness of the physical space, tempered power-law…
In this paper we obtain closed expressions for the probability distribution function, when we consider aggregated risks with multivariate dependent Pareto distributions. We work with the dependent multivariate Pareto type II proposed by…
An opportunistic relay selection based on instantaneous knowledge of channels is considered to increase security against eavesdroppers. The closed-form expressions are derived for the average secrecy rates and the outage probability when…
We report on probability-density-functions (PDF) of the mass density in numerical simulations of highly compressible hydrodynamic flows and the corresponding structure formation of Lagrangian particles advected by the flows. Numerical…
The theory of Extreme Physical Information (EPI) is used to deduce a probability density function (PDF) of a system that exhibits a power law tail. The computed PDF is useful to study and fit several observed distributions in complex…
We report on the distribution spectra of the fluctations in the amount of power injected into a liquid crystal undergoing electroconvective flow. The probability distribution functions (PDFs) of the fluctuations as well as the magnitude of…
The phenomenology of velocity statistics in turbulent flows, up to now, relates to different models dealing with either signed or unsigned longitudinal velocity increments, with either inertial or dissipative fluctuations. In this paper, we…
The estimation of probability density functions (PDF) using approximate maps is a fundamental building block in computational probability. We consider forward problems in uncertainty quantification: the inputs or the parameters of a…
The probability density functions (PDFs) for energy dissipation rates, created from time-series data of grid turbulence in a wind tunnel, are analyzed in a high precision by the theoretical formulae for PDFs within multifractal PDF theory…