ABSTRACT
Abstract A plethora of univariate extreme value mixture models have been developed, which combine a classic tail model with a component to describe the bulk of the distribution. The threshold which defines the tail model support is typically treated as a parameter to be inferred, thus permitting both estimation and uncertainty quantification. These models potentially provide a more objective approach to threshold choice than the traditional graphical diagnostics. This chapter summarises the key features of univariate extreme value mixture models and inference approaches for them. They are presented in a general framework with consistent notation to compare their properties, including a summary of their performance from recent comparative simulation studies. The R packages available on CRAN for implementing these mixture models are outlined. Some advice for developers and users is provided.
