Families of discrete circular distributions with some novel applications
Kanti V. Mardia, Karthik Sriram

TL;DR
This paper introduces new classes of discrete circular distributions motivated by modern circular data, providing four construction methods, analyzing their properties, and demonstrating applications in roulette, smart home data, and changepoint detection.
Contribution
The paper develops four novel methods for constructing discrete circular distributions and explores their properties, especially focusing on marginalized and conditionalized approaches, with practical applications.
Findings
Inherited properties from continuous distributions like von Mises and wrapped Cauchy.
Effective methods for changepoint detection and mixture modeling in circular data.
Applications to roulette, smart home data, and testing for uniformity and serial correlation.
Abstract
Motivated by some cutting edge circular data such as from Smart Home technologies and roulette spins from online and casino, we construct some new rich classes of discrete distributions on the circle. We give four new general methods of construction, namely (i) maximum entropy, (ii) centered wrapping, (iii) marginalized and (iv) conditionalized methods. We motivate these methods on the line and then work on the circular case and provide some properties to gain insight into these constructions. We mainly focus on the last two methods (iii) and (iv) in the context of circular location families, as they are amenable to general methodology. We show that the marginalized and conditionalized discrete circular location families inherit important properties from their parent continuous families. In particular, for the von Mises and wrapped Cauchy as the parent distribution, we examine their…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsBayesian Methods and Mixture Models · Mathematical Dynamics and Fractals · Stochastic processes and statistical mechanics
