Parametric bootstrap edf-based goodness-of-fit testing for sinh–arcsinh distributions
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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 maximum 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 methodology is illustrated in the analysis of data on the body mass index of athletes and the depth of snow on an Antarctic ice floe.
KeywordsAnderson–Darling statistic Logistic distribution Normal distribution Quantile-based estimation Sinh–arcsinh transformation t-distribution
Mathematics Subject Classification62F40 62F03 62F10
I am most grateful to Dr Chris Banks and Professor Paul Garthwaite for access to the snow depth data, and to two referees and an Associate Editor for their careful reading of the original manuscript and helpful suggestions as to how it might be improved. Financial support for the research which led to the production of this paper was received from the Junta de Extremadura and the European Union in the form of grant GR15013.