[1] Abe, T. and Pewsey, A. (2011). Symmetric circular models through duplication and cosine perturbation. Computational Statistics & Data Analysis, 55(12):3271–3282. [2] Abe, T., Shimizu, K., and Pewsey, A. (2010). Symmetric unimodal models for directional data motivated by inverse stereographic projection. Journal of the Japan Statistical Society, 40(1):045–061. [3] Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12:171–178. [4] Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65(2):367–389. [5] Branco, M. D. and Dey, D. K. (2001). A general class of multivariate skew-elliptical distributions. Journal of Multivariate Analysis, 79(1):99–113. [6] Bruderer, B. and Jenni, L. (1990). Migration across the alps. In Bird Migration, pages 60–77. Springer. [7] Cartwright, D. E. (1963). The use of directional spectra in studying the out- put of a wave recorder on a moving ship. In Ocean Wave Spectra, pages 203–218. Englewood Cliffs, NJ: Prentice-Hall. [8] Fern´andez, C. and Steel, M. F. (1998). On Bayesian modeling of fat tails and skewness. Journal of the American Statistical Association, 93(441):359–371. [9] Ferreira, J. T. and Steel, M. F. (2007). A new class of skewed multivariate distributions with applications to regression analysis. Statistica Sinica, pages 505–529. [10] Fisher, N. (1993). Statistical Analysis of Circula Data. Cambridge University Press, London. [11] Genton, M. G. (2004). Skew-elliptical distributions and their applications: a journey beyond normality. CRC Press. [12] Holzmann, H., Munk, A., Suster, M., and Zucchini, W. (2006). Hidden markov models for circular and linear-circular time series. Environmental and Ecological Statistics, 13(3):325–347. [13] Jammalamadaka, S. R. and SenGupta, A. (2001). Topics in Circular Statistics. World Scientific, Singapore. [14] Johnson, N. L., Kotz, S., and Balakrishnan, N. (1995). Continuous Univariate Distributions, Volume 2, 2nd Edition. John Wiley & Sons, New York. [15] Jones, M. C. (2006). A note on rescalings, reparametrizations and classes of distributions. Journal of Statistical Planning and Inference, 136(10):3730–3733. [16] Jones, M. C. and Faddy, M. J. (2003). A skew extension of the t−distribution, with applications. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65(1):159–174. [17] Jones, M. C. and Pewsey, A. (2012a). Inverse batschelet distributions for circular data. Biometrics, 68(1):183–193. [18] Jones, M. C. and Pewsey, A. (2012b). Inverse batschelet distributions for circular data. Biometrics, 68(1):183–193. [19] Kato, S. and Jones, M. (2010). A family of distributions on the circle with links to, and applications arising from, Mobius transformation. ¨ J. Amer. Statist. Assoc., 105:249–262. [20] Kato, S. and Jones, M. (2015). A tractable and interpretable four-parameter family of unimodal distributions on the circle. Biometrika, 102(1):181–190. [21] Ma, Y. and Genton, M. G. (2004). Flexible class of skew-symmetric distributions. Scandinavian Journal of Statistics, 31(3):459–468. [22] Mardia, K. (1972). Statistics of Directional Data. Academic Press, New York. [23] Mardia, K. V. and Jupp, P. E. (2009). Directional Statistics. John Wiley & Sons.