Entropy estimation of multimodal circular distributions.
Li-S; Mnatsakanov-R; Fedorowicz-A; Andrew-ME
Communicating Statistics: Speaking Out and Reaching Out. 2008 JSM Proceedings. Papers presented at the Joint Statistical Meetings, Denver, Colorado, August 3-7, 2008, and other ASA-sponsored Conferences. Alexandria, VA: American Statistical Association, 2008 Aug; :1828-1835
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.
Statistical-analysis; Models; Mathematical-models; Computer-models;
Author Keywords: Entropy; Circular Distribution; Generalized von Mises Distribution; EM Algorithm; KNN; Spacings
Communicating Statistics: Speaking Out and Reaching Out. 2008 JSM Proceedings. Papers presented at the Joint Statistical Meetings, Denver, Colorado, August 3-7, 2008, and other ASA-sponsored Conferences