Distribution of the Distance Between Two Random Points in a Body from R~n

摘要

In the present paper a formula for calculation of the density function f(rho)(x) of the distance between two independent points randomly and uniformly chosen in a bounded convex body D is given. The formula permits to find an explicit form of density function f(rho)(x) for body with known chord length distributions. In particular, we obtain an explicit expression for f(rho)(x) in the case of a ball of diameter d.A simulation model is suggested to calculate empirically the cumulative distribution function of the distance between two points in a body from R-n, where explicit form of the function is hard to obtain. In particular, simulation is performed for balls and ellipsoids in R-n.