PDF of multimodal circular data

[funcosed]

Hi,
I have a data vector that consists of directions measured in an experiment. I wish to create a probability density function. As the data is circular and multimodal I use a kernel density estimate with von Mises distribution (essentially a Gaussian on the unit circle) as the basis function. I fit a von Mises function to each data point and sum the results to obtain a smooth distribution. To obtain a probability density I simply divide each point in the distribution by the integral of the whole distribution. However, my results seem odd after the integration as the maximum value in the pdf is larger than 1. I think it might be related to how I do the integration, I use the trapezoid rule (I work in python so it's numpys trapz command) but I am not sure if this is appropriate for circular data. Has anyone out there had this problem before? any advice??

 

[June Lee]

For N = 4, the Bingham distribution is a distribution over the space of unit quaternions. Since a unit quaternion 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. And for those with talent relative <link deleted> wanting to make World Wide history ...