Skew‐symmetric distributions generated by the distribution function of the normal distribution

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A nonparametric method for estimating asymmetric densities based on skewed Birnbaum–Saunders distributions applied to environmental data (2013, background): “Other classes are the skew-Cauchy, skew-elliptic, skew-normal, skew-slash, and skew-t distributions; see Azzalini and Capitanio (1999, 2003), Arnold and Beaver (2000), Wang and Genton (2006) and Gómez et al. (2007).”
Skew-symmetric distributions and Fisher information -- a tale of two densities (2012, background): “[16], who show that, by combining a Student kernel with ν degrees of freedom and a skewing function of the form 1, Fisher information at δ = 0 is non-singular in general but becomes singular as ν → ∞.”
Bayesian inference for shape mixtures of skewed distributions, with application to regression analysis (2008, methodology): “Consider the conditional representation (22)-(23) of the SN linear regression model (15), with the prior specifications in (24).”