Environmental and Ecological Statistics

, Volume 25, Issue 3, pp 363–385 | Cite as

A new multimodal and asymmetric bivariate circular distribution

  • Fatemeh Hassanzadeh
  • Zeynep Kalaylioglu


Multimodal and asymmetric bivariate circular data arise in several different disciplines and fitting appropriate distribution plays an important role in the analysis of such data. In this paper, we propose a new bivariate circular distribution which can be used to model both asymmetric and multimodal bivariate circular data simultaneously. In fact the proposed density covers unimodality as well as multimodality, symmetry as well as asymmetry of circular bivariate data. A number of properties of the proposed density are presented. A Bayesian approach with MCMC scheme is employed for statistical inference. Three real datasets and a simulation study are provided to illustrate the performance of the proposed model in comparison with alternative models such as finite mixture Cosine model.


Asymmetric distribution Circular bivariate data Multimodal distribution Protein structure Wind direction 



Authors gratefully acknowledge Editor-in-Chief and Reviewers for their valuable comments. The first author is grateful to The Scientific and Technological Research Council of Turkey (TUBITAK) for the support.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of KhansarKhansarIran
  2. 2.Department of StatisticsMiddle East Technical UniversityAnkaraTurkey

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