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Hallin and Ley [Bernoulli 18 (2012) 747-763] investigate and fully characterize the Fisher singularity phenomenon in univariate and multivariate families of skew-symmetric distributions. This paper proposes a refined analysis of the (univariate) problem, showing that singularity can be more or less severe, inducing n1/4 (\"simple singularity\") n⅙ (\"double singularity\"), or n1/8 (\"triple singularity\") consistency rates for the skewness parameter. We show, however, that simple singularity (yielding n⅙ consistency rates), if any singularity at all, is the rule, in the sense that double and triple singularities are possible for generalized skew-normal families only. We also show that higher-order singularities, leading to worse-than-n⅛ rates, cannot occur. Depending on the degree of the singularity, our analysis also suggests a simple reparametrization that offers an alternative to the so-called centred parametrization proposed, in the particular case of skew-normal and skew-f families, by Azzalini [Scand. J. Stat. 12 (1985) 171-178], Arei lano-Val le and Azzalini [J. Multivariate Anal. 113 (2013) 73-90], and DiCiccio and Monti [Quaderni di Statistica 13 (2011) 1-21], respectively.

Multi-level adaptation in end-user development (EUD) is an effective way to enable non-technical end users such as educators to gradually introduce more functionality with increasing complexity to 3D virtual learning environments developed by themselves using EUD approaches. Parameterization, integration, and extension are three levels of adaptation ranging from straightforward to complex in terms of what end users have to understand in order to develop functional software applications, all within reach of end users without special training on programming. A 3D educational application EUD system prototype, iVirtualWorld, has been expanded to support 3D virtual chemistry experiments generation using these three levels of EUD adaptation. An evaluation has been conducted on 18 participants from the education domain, and the results confirmed ease-of-learn, ease-of-use, and usefulness of this solution. Contributions of this paper are 1) a paradigm for applying EUD technologies in 3D virtual learning environment creation; 2) an easy-to-use tool for educators to build customized virtual chemistry experiments; and 3) empirical assessment data for the multi-level adaptation solution.