Inference for grouped data with a truncated skew-Laplace distribution

• Published in: Computational statistics & data analysis 2011-12, Vol.55 (12), p.3218-3231
• Main Authors: Rubio, F.J., Steel, M.F.J.
• Format: Article
• Language: English
• Subjects: Bayesian inference; Bayesian inference Flow cytometry data Glass fibre data Posterior existence Rounding; Distribution theory; Exact sciences and technology; Flow cytometry; Flow cytometry data; General topics; Glass fibre data; Mathematical analysis; Mathematics; Microorganisms; Modelling; Multivariate analysis; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Posterior existence; Probability and statistics; Rounding; Scalars; Sciences and techniques of general use; Skewed distributions; Statistics
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2011.06.002

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. ► We propose a truncated skew-Laplace distribution for modelling rounded observations. ► “Noninformative” benchmark priors are specified. ► Conditions for the existence of the posterior distribution with rounding and various forms of truncation are provided. ► Example concerning microbiological data obtained with flow cytometry for the E. Coli bacterium.