Abstract
Existing circular and toroidal distributions are mostly symmetric; however, many datasets possess asymmetric patterns. Due to the increasing need for asymmetric distributions in recent times, driven by complex modern datasets, in this chapter a new approach is introduced to generate skewed distributions from symmetric distributions, for modeling both circular and toroidal skewed data. This new family of asymmetric distributions, called generalized skew-symmetric distributions, includes some well-known distributions as special cases, such as the circular models of Umbach and Jammalamadaka (Stat Probab Lett 79:659–663, 2009) [24] and Abe and Pewsey (Stat Pap 52:683–707) [1] and the toroidal model of Ameijeiras-Alonso and Ley (Biostatistics, 2020. https://doi.org/10.1093/biostatistics/kxaa039) [2]. General properties of the new models are studied, and we see that the proposed distributions are able to provide wider ranges of skewness as their competitors. To illustrate the practical implementation and usefulness of our new general skewing approach, we compare our models to competitors from the literature on several real datasets.
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Acknowledgements
Christophe Ley’s research is supported by the FWO Krediet aan Navorsers grant with reference number 1510391N. This work was further based upon research supported in part by the National Research Foundation (NRF) of South Africa, SARChI Research Chair UID: 71199; Ref.: IFR170227223754 grant No. 109214; Ref.: SRUG190308422768 Grant No. 120839, and DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa. The opinions expressed and conclusions arrived at are those of the authors and are not necessarily to be attributed to the CoE-MaSS and the NRF. We would like to thank the reviewers for their thoughtful comments and efforts toward improving our manuscript.
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Bekker, A., Nakhaei Rad, N., Arashi, M., Ley, C. (2022). Generalized Skew-Symmetric Circular and Toroidal Distributions. In: SenGupta, A., Arnold, B.C. (eds) Directional Statistics for Innovative Applications. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-19-1044-9_9
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