Entropy Estimation of Multimodal Circular Distributions

• Activity Number: 369
• Type: Contributed
• Date/Time: Wednesday, August 6, 2008 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Shengqiao Li*+ and Robert Mnatsakanov and Adam Fedorowicz and Michael E. Andrew
• Companies: Centers for Disease Control and Prevention and Centers for Disease Control and Prevention and Centers for Disease Control and Prevention and National Institute for Occupational Safety and Health
• Keywords: Entropy ; Circular Distribution ; Generalized von Mises Distribution ; EM Algorithm ; KNN ; Spacings

Abstract

In the entropy estimation problem of multimodal circular distributions, four methods are proposed. They are based on: 1) generalized von Mises (GvM) model; 2) finite mixtures of von Mises (MvM) distributions; 3) circular spacings of order k (KCS), and 4) k-nearest neighbor (KNN) construction. GvM can be skewed and/or multimodal. Its parameters are estimated numerically via MLE approach. In the case of MvM, an EM algorithm is derived and applied to estimate the model parameters. These four methods are compared through simulations. It is shown that the two parametric models and KCS method perform quite well and they are slightly better than KNN estimator in terms of RMSE. KCS approach is very simple and fast; therefore it is recommended in our study. Finally, the rotational entropies of four different dihedral angles of (S, S)-tartaric acid molecule are estimated using these methods.