From the integration of nonsymmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. Motivated by the mathematical curiosity, we show that these generalized functions are suitable to generalize some probability density functions pdfs . A very reliable rank distribution can be conveni...

The diffusion entropy analysis measures the scaling of the probability density function (pdf) of the diffusion process generated by time series imagined as a physical source of fluctuations. The pdf scaling exponent, δ, departs in the non-Gaussian case from the scaling exponent HV evaluated by variance based methods. When δ = 1/(3 − 2HV ) Lévy statistics characterizes the time series. With the ...

The emerging applications of wireless speech communication are demanding increasing levels of performance in noise adverse environments together with the design of high response rate speech processing systems. This is a serious obstacle to meet the demands of modern applications and therefore these systems often needs a noise reduction algorithm working in combination with a precise voice activ...

Properties of velocity circulation in three-dimensional turbulence are studied using data from highresolution direct numerical simulation of Navier-Stokes equations. The probability density function (PDF) of the circulation depends on the area of the closed contour for which circulation is calculated, but not on the shape of the contour. For contours lying within the inertial range, the PDF has...

We present an image representation method which is derived from analyzing Gaussian probability density function (pdf) space using Lie group theory. In our proposed method, images are modeled by Gaussian mixture models (GMMs) which are adapted from a globally trained GMM called universal background model (UBM). Then we vectorize the GMMs based on two facts: (1) components of imagespecific GMMs a...

With the assumption that the bed shear stress fluctuates in a lognormal fashion, the probability density function (pdf) of the standardised bed shear stress is derived as a function of the relative shear stress intensity. The pdf is more skewed with larger relative intensities, but approaches a Gaussian function when the relative intensity is small. The computed pdf agrees well with the reporte...

Novel auxiliary truncated unscented Kalman filtering (ATUKF) is proposed for bearings-only maneuvering target tracking in this paper. In the proposed algorithm, to deal with arbitrary changes in motion models, a modified prior probability density function (PDF) is derived based on some auxiliary target characteristics and current measurements. Then, the modified prior PDF is approximated as a G...

Normal dynamics in a quasi-one-dimensional channel of length L (→∞) of N hard spheres are analyzed. The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W∼D(-γ) for small D, where 0≤γ<1. The initial spheres' density ρ is nonuniform and scales with the distance (from the origin) l as ρ∼l(-α), 0≤α≤1. An approximation for the N-...

[1] Spatial and temporal heterogeneity of ambient natural environments play a significant role in large scale transport phenomena. Uncertainty about spatio‐temporal fluctuations in system parameters (e.g., flow velocity) make deterministic predictions of macroscopic system states (e.g., solute concentration) elusive. Distributions of system states generally exhibit highly non‐Gaussian behavior,...

Finite size scaling in the solar wind magnetic field energy density as seen by WIND Abstract. Statistical properties of the interplanetary magnetic field fluctuations can provide an important insight into the solar wind turbulent cascade. Recently, analysis of the Probability Density Functions (PDF) of the velocity and magnetic field fluctuations has shown that these exhibit non-Gaussian proper...