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Indian Journal of Pure and Applied Mathematics

, Volume 50, Issue 4, pp 953–969 | Cite as

Skew-symmetric circular distributions and their structural properties

  • Mojtaba HatamiEmail author
  • Mohammad Hossein AlamatsazEmail author
Article
  • 12 Downloads

Abstract

A general method of constructing a circular model is to apply transformation to its argument. In this paper, we propose a new transformation in order to construct a large class of new skew-symmetric circular models. We consider a symmetric unimodal distribution as our base model and provide general results for the modality, skewness and shape properties of the resulting circular distributions. The new class enfolds two well-known and common classes of unimodal symmetric and asymmetric circular distributions. The skewness parameter in the new class greatly improves the flexibility of our model to cover symmetric, asymmetric, unimodal and multimodal data. Further, we consider Wrapped Cauchy distribution as a special case for our base distribution and introduce the Skew-Symmetric Wrapped Cauchy (SSWC) distribution, discuss its sub-models and estimate its parameters by the maximum likelihood method. Finally, an application of SSWC distribution and its inferential methods are illustrated using two real data examples.

Key words

Circular statistics argument transformation unimodality peakedness skewness wrapped Cauchy distribution 

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Notes

Acknowledgement

The first author is grateful to the Graduate Office of the University of Isfahan, Iran for their support.

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Copyright information

© Indian National Science Academy 2019

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of IsfahanIsfahanIran

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