Among all measures of independence between random variables, mutual information is the only one that is based on information theory. Mutual information takes into account of all kinds of dependencies between variables, i.e., both the linear and non-linear dependencies. In this paper we have classified some well-known bivariate distributions into two classes of distributions based on their mutua...

The Shannon effect states that “almost all” Boolean functions have a complexity close to the maximal possible for the uniform probability distribution. In this paper we use some probability distributions on functions, induced by random expressions, and prove that this model does not exhibit the Shannon effect.

background and purpose: the identification of genetics risk factors of human diseases is very important. this study is conducted to model the allele frequencies (afs) of alzheimer’s disease. materials and methods: in this study, several candidate probability distributions are fitted on a data set of alzheimer’s disease genetic risk factor. unknown parameters of the considered distributions are ...

The aim of this paper, we use Stein’s method and the w-function associated with the Yule random variable to obtain a non-uniform bound for the point metric of the Yule and geometric distributions. Three numerical examples are provided to illustrate the obtained result. AMS Subject Classification: 62E17, 60F05

Plan 1. Linnik and creation of the Leningrad school 2. Linnik’s students 3. 1951 4. Unimodal distributions 5. Classical limit theorems a) moment conditions for given convergence rate b) fast convergence rates in CLT c) Chebyshev-Cramér asymptotic expansions 6. Weak dependence a) uniform mixing condition b) central limit theorem under uniform mixing condition c) continued fractions d) central li...

Wireless networks in which the node locations are random are best modelled as random geometric graphs (RGGs). In addition to their extensive application in the modelling of wireless networks, RGGs are finding many new applications and are being studied in their own right. In this paper we first provide a brief introduction to the issues of interest in random wireless networks. We then discuss s...

We give sharp, uniform estimates for the probability that a random walk of n steps on the reals avoids a half-line [y,∞) given that it ends at the point x. The estimates hold for general continuous or lattice distributions provided the 4th moment is finite.

2 Random Variable Generation 5 2.1 Basic Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 Congruential Generators . . . . . . . . . . . . . . . . . 6 2.1.2 The Kiss Generator . . . . . . . . . . . . . . . . . . . . 8 2.1.3 Beyond Uniform Distributions . . . . . . . . . . . . . . 10 2.2 Transformation methods . . . . . . . . . . . . . . . . . . . . . 11 2.3 Accept-Reject Met...