• Comparison and classification of flexible distributions for multivariate skew and heavy-tailed data

      Babic, Sladana; Ley, Christophe; Veredas, David (Symmetry, 2019)
      We present, compare and classify popular families of flexible multivariate distributions. Our classification is based on the type of symmetry (spherical, elliptical, central symmetry or asymmetry) and the tail behaviour (a single tail weight parameter or multiple tail weight parameters). We compare the families both theoretically (relevant properties and distinctive features) and with a Monte Carlo study (comparing the fitting abilities in finite samples).
    • Flexible models for complex data with applications

      Ley, Christophe; Babic, Sladana; Craens, Domien (Annual Review of Statistics and Its Application, 2021)
      Probability distributions are the building blocks of statistical modeling and inference. It is therefore of the utmost importance to know which distribution to use in what circumstances, as wrong choices will inevitably entail a biased analysis. In this article, we focus on circumstances involving complex data and describe the most popular flexible models for these settings. We focus on the following complex data: multivariate skew and heavy-tailed data, circular data, toroidal data, and cylindrical data. We illustrate the strength of flexible models on the basis of concrete examples and discuss major applications and challenges.