as of the von Mises above. Wrapped normal distribution The pdf of the wrapped normal distribution (WN) is: where μ and σ are the mean and standard deviation of the unwrapped distribution, respectively and is the Jacobi theta function: where and Wrapped Cauchy distribution The pdf of the wrapped Cauchy distribution (WC) is: where is the scale factor and is the peak position. Wrapped Lévy distribution The pdf of the wrapped Lévy distribution (WL) is: where the value of the summand is taken to be zero when , is the scale factor and is the location parameter. Distributions on higher-dimensional manifolds There also exist distributions on the two-dimensional sphere (such as the Kent distribution), the N-dimensional sphere (the von Mises–Fisher distribution) or the torus (the bivariate von Mises distribution). The matrix von Mises–Fisher distribution is a distribution on the Stiefel manifold, and can be used to construct probability distributions over rotation matrices. The Bingham distribution is a distribution over axes in N dimensions, or equivalently, over points on the (N − 1)-dimensional sphere with the antipodes identified. For example, if N = 2, the axes are undirected lines through the origin in the plane. In this case, each axis cuts the unit circle in the plane (which is the one-dimensional sphere) at two points that are each other's antipodes. For N = 4, the Bingham distribution is a distribution over the space of unit quaternions (versors). Since a versor corresponds to a rotation matrix, the Bingham distribution for N = 4 can be used to construct probability distributions over the space of rotations, just like the Matrix-von Mises–Fisher distribution. These distributions are for example used in geology, crystallography and bioinformatics. Moments The raw vector (or trigonometric) moments of a circular distribution are defined as where is any interval of length , is the PDF of the circular distribution, and . Since the integral is unity, and the integration interval is finite, it follows that the moments of any circular distribution are always finite and well defined. Sample moments are analogously defined: The population resultant vector, length, and mean angle are defined in analogy with the corresponding sample parameters. In addition, the lengths of the higher moments are defined as: while the angular parts of the higher moments are just . The lengths of all moments will lie between 0 and 1. Measures of location and spread Various measures of central