Given n (discrete or continuous) random variables Xi, the (2 n − 1)-dimensional vector obtained by evaluating the joint entropy of all non-empty subsets of {X1,. .. , Xn} is called an entropic vector. Determining the region of entropic vectors is an important open problem with many applications in information theory. Recently, it has been shown that the entropy regions for discrete and continuo...

let x1;x2;...;xn have a jointly multivariate exchangeable normal distribution. in this work we investigate another proof of the independence of x and s2 using order statistics. we also assume that (xi ; yi); i =1; 2;...; n; jointly distributed in bivariate normal and establish the independence of the mean and the variance of concomitants of order statistics.

We study the rare event behavior of the workload process in a transitory queue, where the arrival epochs (or ‘points’) of a finite number of jobs are assumed to be the ordered statistics of independent and identically distributed (i.i.d.) random variables. The service times (or ‘marks’) of the jobs are assumed to be i.i.d. random variables with a general distribution, that are jointly independe...

‎The main purpose of this note is to establish some bounds in Poisson approximation for row-wise arrays of independent geometric distributed random variables using the operator method‎. ‎Some results related to random sums of independent geometric distributed random variables are also investigated.

A number of basic properties about circularly-symmetric Gaussian random vectors are stated and proved here. These properties are each probably well known to most researchers who work with Gaussian noise, but I have not found them stated together with simple proofs in the literature. They are usually viewed as too advanced or too detailed for elementary texts but are used (correctly or incorrect...

We present a simple, geometric method to construct Fieller’s exact confidence sets for ratios of jointly normally distributed random variables. Contrary to previous geometric approaches in the literature, our method is valid in the general case where both sample mean and covariance are unknown. Moreover, not only the construction but also its proof are purely geometric and elementary, thus givi...