We consider a family of chaotic skew tent maps. The skew tent map is a two-parameter, piecewise-linear, weakly-unimodal, map of the interval Fa;b. We show that Fa;b is Markov for a dense set of parameters in the chaotic region, and we exactly nd the probability density function (pdf), for any of these maps. It is well known, [1], that when a sequence of transformations has a uniform limit F , a...

Introduction: Probability density function (PDF) estimation is a very important issue in several interesting areas, such as blind signal processing and adaptive data processing. The estimation of the PDF or the cumulative density function (CDF) through use of an easy and fast method becomes a very important task. Several approaches exist [1] such as maximum likelihood estimation, kernel estimat...

This note presents some investigations of smoothing routines for the estimation of PDF, specifically the HBOOK SMOOTH, MLP-fit and a Gaussian Kernel estimator. It presents some tests on the over-training, or more generally the accuracy of the PDF. No technique is perfect, but the kernel estimator gives the best results in a series of tests, and it is recommended that it be tried for the Higgs s...

This paper presents new envelope PDF's (probability density functions) that describe smallscale, local area fading experienced by narrowband wireless receivers. The paper develops novel PDF's that describe the local area fading of two coherent multipath components in the presence of other diffuse propagating waves. Analytical expressions, graphical analysis, and applicability of the PDF's are p...

We show a general relation between the spatially disjoint product of probability density functions and the sum of their Fisher information metric tensors. We then utilise this result to give a method for constructing the probability density functions for an arbitrary Riemannian Fisher information metric tensor. We note further that this construction is extremely unconstrained, depending only on...

We show that the generating functions of the generalized Catalan numbers can be identified with the moment generating functions of probability density functions related to the Brownian motion stochastic process. Specifically, the probability density functions are exponential mixtures of inverse Gaussian (EMIG) probability density functions, which arise as the first passage time distributions to...

We develop a theoretical methodology for estimating joint probability density functions from marginals by, transforming the set of random variables into another set of independent random variables is necessary. To test this theory in practice, we developed a software application which implemented a reduced form of this methodology, and worked well with several datasets. Finally, we discuss how ...

Fox’s H-function provide a unified and elegant framework to tackle several physical phenomena. We solve the space fractional diffusion equation on the real line equipped with a delta distribution initial condition and identify the corresponding H-function by studying the small x expansion of the solution. The asymptotic expansions near zero and infinity are expressed, for rational values of the...