We generalize the well-known Laguerre series approach to approximate multivariate probability density functions (PDFs) using multidimensional Laguerre polynomials. The generalized Laguerre series, which is defined around a Gamma PDF, is suited for simulating high complex natural phenomena that deviate from Gaussianity. Combining the multivariate Laguerre approximation and Bayes theorem, an appr...

We use the spherical evolution approximation to investigate nonlinear evolution from the non-Gaussian initial conditions characteristic of the local fnl model. We provide an analytic formula for the nonlinearly evolved probability distribution function of the dark matter which shows that the underdense tail of the nonlinear PDF in the fnl model should differ significantly from that for Gaussian...

Recently, one of the authors, studying a model for turbulent diffusion involving a large-scale velocity field rapidly fluctuating in time, rigorously demonstrated intermittency in a diffusing scalar field by exhibiting broader than Gaussian tails in the scalar PDF. Here, we explore this model further with exact formulas within the context of general initial data possessing both a mean and a flu...

This thesis is devoted to study blind source separation techniques applied to multiuser processing in digital communications. Using probability density function (pdf) estimation strategies, two multiuser processing methods are proposed. They aim for recovering transmitted signal by using the Kullback-Leibler similarity measure between the signals pdf and a parametric model that contains the sig...

We develop a powerful probabilistic framework for the local characterization of surfaces and edges in range images, which is useful in many applications of computer vision, such as filtering, edge detection, feature extraction, and classification. We use the geometrical nature of the data to derive an analytic expression for the joint probability density function (pdf) for the random variables ...

This figure "fig2-1.png" is available in "png"" format from: This figure "fig3-1.png" is available in "png"" format from: This figure "fig4-1.png" is available in "png"" format from: This figure "fig5-1.png" is available in "png"" format from: This figure "fig6-1.png" is available in "png"" format from: { 15 { FIGURE CAPTIONS Fig. 1.| The PDF of the density eld from the 1.2 Jy IRAS galaxy catal...

0

The two-dimensional (2-D) Gaussian Q-function has been used in evaluating the error and outage probability performance of wireless communication systems. The 2-D Gaussian Q-function representation has been proposed to compute the probability of an arbitrary wedge-shaped region in the presence of additive white Gaussian noise (AWGN) [1]-[5]. Alouini and others developed the 2-D Gaussian Q-functi...