ABSTRACT
This chapter concentrates on the behaviour of distributional tails. It classifies the tails of continuous and discrete distributions. The chapter provides methods for identifying the tail of the distribution of the response variable of a given data set. It introduces the basic concepts of tail behaviour and classifies continuous Generalized Additive Models for Location Scale, and Shape family distributions into categories according to their tail behaviour. The tail of a distribution is of great importance when the interest is to investigate rare events. Value at risk and Expected shortfall are well-known concepts in financial analysis and are affected by how the tail of the response distribution behaves. The important point is the use of a heavy-tailed distribution to model heavy-tailed response variable results in robust modeling rather than robust estimation.
