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Inference for grouped data with a truncated skew-Laplace distribution

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  • Rubio, F.J.
  • Steel, M.F.J.

Abstract

The skew-Laplace distribution has been used for modelling particle size with point observations. In reality, the observations are truncated and grouped (rounded). This must be formally taken into account for accurate modelling, and it is shown how this leads to convenient closed-form expressions for the likelihood in this model. In a Bayesian framework, "noninformative" benchmark priors, which only require the choice of a single scalar prior hyperparameter, are specified. Conditions for the existence of the posterior distribution are derived when rounding and various forms of truncation are considered. The main application focus is on modelling microbiological data obtained with flow cytometry. However, the model is also applied to data often used to illustrate other skewed distributions, and it is shown that our modelling compares favourably with the popular skew-Student models. Further examples with simulated data illustrate the wide applicability of the model.

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File URL: http://www.sciencedirect.com/science/article/pii/S0167947311002039
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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 55 (2011)
Issue (Month): 12 (December)
Pages: 3218-3231

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Handle: RePEc:eee:csdana:v:55:y:2011:i:12:p:3218-3231

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Web page: http://www.elsevier.com/locate/csda

Related research

Keywords: Bayesian inference Flow cytometry data Glass fibre data Posterior existence Rounding;

References

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  1. Trindade, A. Alexandre & Zhu, Yun, 2007. "Approximating the distributions of estimators of financial risk under an asymmetric Laplace law," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3433-3447, April.
  2. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
  3. H. Schneeweiss & J. Komlos & A. Ahmad, 2010. "Symmetric and asymmetric rounding: a review and some new results," AStA Advances in Statistical Analysis, Springer, vol. 94(3), pages 247-271, September.
  4. Fernández, C. & Steel, M.F.J., 1997. "Reference Priors for the General Location-Scale Model," Discussion Paper 1997-105, Tilburg University, Center for Economic Research.
  5. 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.
  6. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2006. "A Constructive Representation of Univariate Skewed Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 823-829, June.
  7. Thaís C. O. Fonseca & Marco A. R. Ferreira & Helio S. Migon, 2008. "Objective Bayesian analysis for the Student-t regression model," Biometrika, Biometrika Trust, vol. 95(2), pages 325-333.
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