Anisotropic Buffon’s needle problems

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 probability