A Laplace-based model with flexible tail behavior

Cristina Tortora*, Brian C. Franczak, Luca Bagnato, Antonio Punzo

*Corresponding author

Research output: Contribution to journalArticle


The proposed multiple scaled contaminated asymmetric Laplace (MSCAL) distribution is an extension of the multivariate asymmetric Laplace distribution to allow for a different excess kurtosis on each dimension and for more flexible shapes of the hyper-contours. These peculiarities are obtained by working on the principal component (PC) space. The structure of the MSCAL distribution has the further advantage of allowing for automatic PC-wise outlier detection – i.e., detection of outliers separately on each PC – when convenient constraints on the parameters are imposed. The MSCAL is fitted using a Monte Carlo expectation-maximization (MCEM) algorithm that uses a Monte Carlo method to estimate the orthogonal matrix of eigenvectors. A simulation study is used to assess the proposed MCEM in terms of computational efficiency and parameter recovery. In a real data application, the MSCAL is fitted to a real data set containing the anthropometric measurements of monozygotic/dizygotic twins. Both a skewed bivariate subset of the full data, perturbed by some outlying points, and the full data are considered.
Original languageEnglish
Pages (from-to)1-19
Number of pages19
Publication statusPublished - 2024


  • Contaminated distributions
  • Directional outlier detection
  • Monte Carlo expectation-maximization algorithm
  • Multiple scaled distributions
  • Normal variance-mean mixtures


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