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Problems of inference for Azzalini's skewnormal distribution

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Author Info
Arthur Pewsey
Abstract

This paper considers various unresolved inference problems for the skewnormal 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.

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Article provided by Taylor and Francis Journals in its journal Journal of Applied Statistics.

Volume (Year): 27 (2000)
Issue (Month): 7 (September)
Pages: 859-870
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Handle: RePEc:taf:japsta:v:27:y:2000:i:7:p:859-870

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Barry Arnold & Robert Beaver & Richard Groeneveld & William Meeker, 1993. "The nontruncated marginal of a truncated bivariate normal distribution," Psychometrika, Springer, vol. 58(3), pages 471-488, September. [Downloadable!] (restricted)
  2. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602. [Downloadable!] (restricted)
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  1. Anna Clara Monti, 2003. "A note on the estimation of the skew normal and the skew exponential power distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 205-219. [Downloadable!]
  2. Adelchi Azzalini & Monica Chiogna, 2004. "Some results on the stress–strength model for skew-normal variates," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 315-326. [Downloadable!]
  3. Yakov Y. Nikitin & Irina Peaucelle, 2004. "Efficiency and local optimality of nonparametric tests based on U- and V-statistics," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 185-200. [Downloadable!]
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