Sankhya A

, Volume 79, Issue 1, pp 133–157 | Cite as

A General Approach for Obtaining Wrapped Circular Distributions via Mixtures

  • S. Rao Jammalamadaka
  • Tomasz J. KozubowskiEmail author


We show that the operations of mixing and wrapping linear distributions around a unit circle commute, and can produce a wide variety of circular models. In particular, we show that many wrapped circular models studied in the literature can be obtained as scale mixtures of just the wrapped Gaussian and the wrapped exponential distributions, and inherit many properties from these two basic models. We also point out how this general approach can produce flexible asymmetric circular models, the need for which has been noted by many authors.

Keywords and phrases

Circular data Wrapped distributions Mixtures Wrapped normal Wrapped exponential Scale mixtures 

AMS (2010) Subject Classification

Primary 62H11 Secondary 60E05, 62E10 


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Copyright information

© Indian Statistical Institute 2017

Authors and Affiliations

  1. 1.Department of Statistics & Applied ProbabilityUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Department of Mathematics & StatisticsUniversity of NevadaRenoUSA

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