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The sinh-arcsinhed logistic family of distributions: properties and inference

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  • Arthur Pewsey
  • Toshihiro Abe

Abstract

The sinh-arcsinh transform is used to obtain a flexible four-parameter model that provides a natural framework with which to perform inference robust to wide-ranging departures from the logistic distribution. Its basic properties are established and its distribution and quantile functions, and properties related to them, shown to be highly tractable. Two important subfamilies are also explored. Maximum likelihood estimation is discussed, and reparametrisations designed to reduce the asymptotic correlations between the maximum likelihood estimates provided. A likelihood-ratio test for logisticness, which outperforms standard empirical distribution function based tests, follows naturally. The application of the proposed model and inferential methods is illustrated in an analysis of carbon fibre strength data. Multivariate extensions of the model are explored. Copyright The Institute of Statistical Mathematics, Tokyo 2015

Suggested Citation

  • Arthur Pewsey & Toshihiro Abe, 2015. "The sinh-arcsinhed logistic family of distributions: properties and inference," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(3), pages 573-594, June.
    • Handle: RePEc:spr:aistmt:v:67:y:2015:i:3:p:573-594
    DOI: 10.1007/s10463-014-0465-x
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    References listed on IDEAS

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    1. Jones, M. C. & Rosco, J. F. & Pewsey, Arthur, 2011. "Skewness-Invariant Measures of Kurtosis," The American Statistician, American Statistical Association, vol. 65(2), pages 89-95.
    2. M. C. Jones & M. J. Faddy, 2003. "A skew extension of the t‐distribution, with applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 159-174, February.
    3. M. C. Jones & Arthur Pewsey, 2009. "Sinh-arcsinh distributions," Biometrika, Biometrika Trust, vol. 96(4), pages 761-780.
    4. Saralees Nadarajah, 2009. "The skew logistic distribution," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 93(2), pages 187-203, June.
    5. J. Rosco & M. Jones & Arthur Pewsey, 2011. "Skew t distributions via the sinh-arcsinh transformation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 630-652, November.
    6. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
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    Cited by:

    1. Arthur Pewsey, 2018. "Parametric bootstrap edf-based goodness-of-fit testing for sinh–arcsinh distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 147-172, March.

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