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.

Keywords:

• Bivariate beta distribution
• Expected distance
• Hypergeometric function
• Non central moments
• Rectangular cities

Mathematics Subject Classification:

• 62P12
• 62H99
• 90B06
• 90C15
• 62P10

Acknowledgment

The authors are grateful to a referee for the helpful comments.