Four-parameter sinh–arcsinh classes provide flexible distributions with
which to model skew, as well as light- or heavy-tailed, departures from a symmetric
base distribution. A quantile-based method of estimating their parameters is proposed
and the resulting estimates advocated as starting values from which to initiate maxi-
mum likelihood estimation. Parametric bootstrap edf-based goodness-of-fit tests for
sinh–arcsinh distributions are proposed, and their operating characteristics for small- to
medium-sized samples explored in Monte Carlo experiments. The developed method-
ology is illustrated in the analysis of data on the body mass index of athletes and the
depth of snow on an Antarctic ice floe.

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• Parametric bootstrap edf-based goodness-of-fit testing for sinh–arcsinh distributions