We introduced a random vector , where has Poisson distribution and are minimum of independent and identically distributed exponential random variables. We present fundamental properties of this vector such as PDF, CDF and stochastic representations. Our results include explicit formulas for marginal and conditional distributions, moments and moments generating functions. We also derive moments ...

Let Ω be a compact convex set in Euclidean n-space with nonempty interior. Random triangles are defined here by selecting three independent uniformly distributed points in Ω to be vertices. Generating such points for (n,Ω) = (2,unit square) or (n,Ω) = (3,unit cube) is straightforward. For (n,Ω) = (2,unit disk) or (n,Ω) = (3,unit ball), we use the following result [1]. Let X1, X2, X3, Y1, Y2, Y3...

In this paper systems of functional equations in infinitely many variables arising in combinatorial enumeration problems are studied. We prove sufficient conditions under which the combinatorial random variables encoded in the generating functions of the system tend to an infinite dimensional Gaussian limiting distribution.