As is well known, a continuous parameter process with mutually independent random variables is not jointly measurable in the usual sense. This paper proposes an extension of the usual product measure-theoretic framework, using a natural “one-way Fubini” property. When the random variables are independent even in a very weak sense, this property guarantees joint measurability and defines a uniqu...

Abstract. A methodology is developed to assign, from an observed sample, a joint-probability distribution to a set of continuous variables. The algorithm proposed performs this assignment by mapping the original variables onto a jointly-Gaussian set. The map is built iteratively, ascending the log-likelihood of the observations, through a series of steps that move the marginal distributions alo...

In this note we continue the study of gaps in samples of geometric random variables originated in Hitczenko and Knopfmacher [Gap-free compositions and gap-free samples of geometric random variables. Discrete Math. 294 (2005) 225–239] and continued in Louchard and Prodinger [The number of gaps in sequences of geometrically distributed random variables, Preprint available at 〈http://www.ulb.ac.be...

A new algorithm for generating two positively correlated Beta-distributed random variables with known marginal distributions and a speci*ed correlation is provided. The paired Betadistributed random variables are generated from ratios of independent standard Gamma distributions. A positive correlation is achieved by introducing two shared standard Gamma distributed random variables. Parameters ...

Consider a Gaussian process {Xt}t∈T for some index set T . This is a collection of jointly Gaussian random variables, meaning that every finite linear combination of the variables has a Gaussian distribution. We will additionally assume that the process is centered, i.e. E(Xt) = 0 for all t ∈ T . It is well-known that such a process is completely characterized by the covariances {E(XsXt)}s,t∈T ...

1.0 Rayleigh Distribution Using central limit theorem arguments, one can show that the I and Q channels on a mobile radio multipath fading channel are independent Gaussian (normal) random variables. Jakes [1] and others show that the envelope of two independent and identically distributed (iid) Gaussian random variables is Rayleigh distributed.1 Probability Density Function (pdf) (usual form fo...