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The Sichel model and the mixing and truncation order

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  • Xavier Puig
  • Josep Ginebra
  • Marti Font

Abstract

The analysis of word frequency count data can be very useful in authorship attribution problems. Zero-truncated generalized inverse Gaussian-Poisson mixture models are very helpful in the analysis of these kinds of data because their model-mixing density estimates can be used as estimates of the density of the word frequencies of the vocabulary. It is found that this model provides excellent fits for the word frequency counts of very long texts, where the truncated inverse Gaussian-Poisson special case fails because it does not allow for the large degree of over-dispersion in the data. The role played by the three parameters of this truncated GIG-Poisson model is also explored. Our second goal is to compare the fit of the truncated GIG-Poisson mixture model with the fit of the model that results from switching the order of the mixing and truncation stages. A heuristic interpretation of the mixing distribution estimates obtained under this alternative GIG-truncated Poisson mixture model is also provided.

Suggested Citation

  • Xavier Puig & Josep Ginebra & Marti Font, 2010. "The Sichel model and the mixing and truncation order," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1585-1603.
    • Handle: RePEc:taf:japsta:v:37:y:2010:i:9:p:1585-1603
    DOI: 10.1080/02664760903093617
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    References listed on IDEAS

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    1. Alex Riba & Josep Ginebra, 2006. "Diversity of vocabulary and homogeneity of literary style," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(7), pages 729-741.
    2. Ginebra, Josep & Puig, Xavier, 2010. "On the measure and the estimation of evenness and diversity," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2187-2201, September.
    3. H. S. Sichel, 1985. "A bibliometric distribution which really works," Journal of the American Society for Information Science, Association for Information Science & Technology, vol. 36(5), pages 314-321, September.
    4. Alex Riba & Josep Ginebra, 2005. "Change-point estimation in a multinomial sequence and homogeneity of literary style," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(1), pages 61-74.
    5. D. I. Holmes, 1992. "A Stylometric Analysis of Mormon Scripture and Related Texts," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 155(1), pages 91-120, January.
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    Cited by:

    1. Jordi Valero & Josep Ginebra & Marta Pérez-Casany, 2012. "Extended Truncated Tweedie-Poisson Model," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 811-829, September.

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