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Problems of inference of Azzalini’s skew-normal distribution. (English) Zbl 1076.62514
Summary: This paper considers various unresolved inference problems for the skew-normal distribution. We give reasons as to why the direct parameterization should not be used as a general basis for estimation, and consider method of moments and maximum likelihood estimation for the distribution’s centred parameterization. Large sample theory results are given for the method of moments estimators, and numerical approaches for obtaining maximum likelihood estimates are discussed. Simulation is used to assess the performance of the two types of estimation. We also present procedures for testing for departures from the limiting folded normal distribution. Data on the percentage body fat of elite athletes are used to illustrate some of the issues raised.
Reviewer: Reviewer (Berlin)

MSC:
62F10 Point estimation
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