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. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 8 is March 8, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.