Sine-skewed circular distributions

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On a class of circulas: copulas for circular distributions (2015, background): “Examples of f1 or f2 for which these algorithms would be advantageous include the sine-skewed wrapped Cauchy distribution (Umbach and Jammalamadaka 2009; Abe and Pewsey 2011) and many wrapped distributions.”
Phase Reconstruction from Amplitude Spectrograms Based on Von-Mises-Distribution Deep Neural Network (2018, methodology): “Other possible ways are to use an asymmetric distribution [18] and mixture model.”
On Families of Distributions with Shape Parameters (2015, unknown): “…but here will be written as a two-parameter ‘arctan-tan’ transformation, Family 1 on C is usually represented by the sine-skewed distributions (Umbach & Jammalamadaka, 2009, Abe & Pewsey, 2011) which correspond to w ( θ ) = w B ( θ ) = (1+ ν sin θ ); this w satisﬁes (2) but is not monotone.”
A tractable, parsimonious and flexible model for cylindrical data, with applications (2015, methodology): “The marginal density of the circular component Θ from pdf (1) is given by which is the sine-skewed wrapped Cauchy distribution ([2]), a ﬂexible extension of the symmetric wrapped Cauchy distribution.”