Related papers: The relationship between extremum statistics and u…
Consider randomly picked points inside the n-dimensional unit hypersphere centered at the origin of the Cartesian coordinate system. The Cartesian coordinates of the points are random variables, which form an n-dimensional vector for each…
In this article we generalize the classical Edgeworth expansion for the probability density function (PDF) of sums of a finite number of symmetric independent identically distributed random variables with a finite variance to sums of…
The non-Gaussian normal diffusion, i.e., the probability distribution function (PDF) is non-Gaussian but the mean squared displacement (MSD) depends on time linearly, has been observed in particle motions. Here we show by numerical…
A step by step procedure to derive analytically the exact dynamical evolution equations of the probability density functions (PDF) of well known kinetic wealth exchange economic models is shown. This technique gives a dynamical insight into…
Anomalous dynamics characterized by non-Gaussian probability distributions (PDFs) and/or temporal long-range correlations can cause subtle modifications of conventional fluctuation relations. As prototypes we study three variants of a…
We study local power fluctuations in numerical simulations of stationary, homogeneous, isotropic turbulence in two and three dimensions with Gaussian forcing. Due to the near-Gaussianity of the one-point velocity distribution, the…
Plasma density fluctuations in the edge plasma of the RFX-mod device are measured through the Gas Puffing Imaging Diagnostics. Statistical features of the signal are quantified in terms of the Probability Distribution Function (PDF), and…
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 Hessian method is widely applied in the global analysis of parton distribution functions (PDFs), which uses a set of orthogonal eigenvectors to give predictions of a physical observable. Its uncertainty is estimated based on the…
We introduce a method for calculating the probability density function (PDF) of a turbulent density field in three dimensions using only information contained in the projected two-dimensional column density field. We test the method by…
The normal distribution is used as a unified probability distribution, however, our researcher found that it is not good agreed with the real-life dynamical system's data. We collected and analyzed representative naturally occurring data…
We consider the statistics of light amplitude fluctuations for the propagation of a laser beam subjected to multiple filamentation in an amplified Kerr media, with both linear and nonlinear dissipation. Dissipation arrests the catastrophic…
In a recent letter, Christian Beck described a theoretical link between a family of stochastic differential equations and the probability density functions (PDF) derived from the formalism of nonextensive statistical mechanics. He applied…
In probability density function (PDF) methods a transport equation is solved numerically to compute the time and space dependent probability distribution of several flow variables in a turbulent flow. The joint PDF of the velocity…
We discuss the non-self-averaging phenomena in the critical point of weakly disordered Ising ferromagnet. In terms of the renormalized replica Ginzburg-Landau Hamiltonian in dimensions D <4, we derive an explicit expression for the…
The late universe contains a wealth of information about fundamental physics and gravity, wrapped up in non-Gaussian fields. To make use of as much information as possible it is necessary to go beyond two-point statistics. Rather than going…
We introduce the position-dependent probability distribution function (PDF) of the smoothed matter field as a cosmological observable. In comparison to the PDF itself, the spatial variation of the position-dependent PDF is simpler to model…
What is the size of the most massive object one expects to find in a survey of a given volume? In this paper, we present a solution to this problem using Extreme-Value Statistics, taking into account primordial non-Gaussianity and its…
The one-point probability distribution function (PDF) of the matter density field in the universe is a fundamental property that plays an essential role in cosmology for estimates such as gravitational weak lensing, non-linear clustering,…
We study density fluctuations in supersonic turbulence using both theoretical methods and numerical simulations. A theoretical formulation is developed for the probability distribution function (PDF) of the density at steady state,…