A new asymmetric generalisation of the t-distribution

Abstract

A 6-parameter fat-tailed distribution is proposed that generalises the t-distribution and allows asymmetry of scale and also of tail power, whilst avoiding the discontinuity of the second derivative of the split-t (AST) distribution. With the sixth parameter set to unity and no asymmetry, the distribution reduces to a t-distribution, but with the sixth parameter reduced, fatter tails than those of the t-distribution are allowed (the tails start earlier) and the distribution generalises Johnson's $S_U$ distribution. Data fitting is illustrated with examples.