The t family and their close and distant relations

Student’s t distribution arose, of course, and has huge application, as a normal-based sampling distribution. In modern times, the t distribution has also found considerable use as a symmetric heavy-tailed distribution for em-pirical data modelling. In this the centenary year of Student’s introduction of the t distribution, this paper constitutes a personal — and sometimes some-what tangential — tribute to the Student-t family of distributions, by way of an exploration of some of its close and not-so-close relations. I start with a brief reminder of the (symmetric) Student-t family, with particular focus on the t distribution on two degrees of freedom which turns out to play an important role in what follows. The “close relations ” of the t distribution in-clude a number of ‘skew-t ’ distributions, of which I shall briefly introduce and comment on three. The “distant relations ” of the t distribution are a further trio of four-parameter families of distributions allowing control of skewness and tailweights, with particular emphasis on members of the families with (t-like) ‘power ’ density tails