Efficient maximum approximated likelihood inference for Tukey's g-and-h distribution

Ganggang Xu*, Marc G. Genton

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


Abstract Tukey's g-and-h distribution has been a powerful tool for data exploration and modeling since its introduction. However, two long standing challenges associated with this distribution family have remained unsolved until this day: how to find an optimal estimation procedure and how to make valid statistical inference on unknown parameters. To overcome these two challenges, a computationally efficient estimation procedure based on maximizing an approximated likelihood function of Tukey's g-and-h distribution is proposed and is shown to have the same estimation efficiency as the maximum likelihood estimator under mild conditions. The asymptotic distribution of the proposed estimator is derived and a series of approximated likelihood ratio test statistics are developed to conduct hypothesis tests involving two shape parameters of Tukey's g-and-h distribution. Simulation examples and an analysis of air pollution data are used to demonstrate the effectiveness of the proposed estimation and testing procedures.

Original languageEnglish (US)
Article number6098
Pages (from-to)78-91
Number of pages14
JournalComputational Statistics and Data Analysis
StatePublished - Jul 2 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier B.V.


  • Approximated likelihood ratio test
  • Computationally efficient
  • Maximum approximated likelihood estimator
  • Skewness
  • Tukey's g-and-h distribution

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics
  • Statistics and Probability
  • Computational Theory and Mathematics


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