Distance Between Bivariate Beta Random Points in Two Rectangular Cities

Abstract

In this article, we consider the distance between two independent bivariate beta distributed random points, one from each of the two rectangular cities. The expected distance between these two random points is obtained as an infinite series of the non central moments of the squared distance. These non central moments can be written in terms of the joint moments of the bivariate beta distribution that involve the hypergeometric function 3 F 2 . A computer program is then written for computing the expected distance. Verifications and simulations are also performed. The even and odd moments of the distance are presented as well.

Non-Uniform Random Number Generation from Arbitrary Bivariate Distribution in Polygonal Area

“…In the literature, the rejection method or the inversion method from univariate and bivariate probability density functions are the most commonly used non-uniform random number generation algorithms [11,14,15,16]. Particularly, while generating non-uniform random numbers from bivariate probability density function, the limit of the probability density functions is defined as rectangular [17,18,19,20]. If the non-uniform random numbers are generated from a bivariate probability density function in an arbitrary area (polygon), then the distribution bounded within the area will be uniform.…”