Anisotropic Buffon’s needle problems

Abstract

In this paper, we investigate anisotropic extensions of the classical Buffon’s needle problem. In particular, we study the cases where the angle between the needle and a fixed reference direction follows a triangular, a trapezoidal, a wrapped exponential, or a Von Mises distribution law. Within the first two cases, we examine both the oriented and non-oriented needle problems, while within the latter two cases, we study the oriented needle problem exclusively. For the examined distributions, we also determine the minimum and the maximum probabilit