Computational Statistics https://doi.org/10.1007/s00180-020-01025-8 ORIGINAL PAPER Finite mixtures of skew Laplace normal distributions with random skewness Fatma Zehra Do ˘ gru 1 · Olcay Arslan 2 Received: 29 November 2019 / Accepted: 14 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract In this paper, the shape mixtures of the skew Laplace normal (SMSLN) distribution is introduced as a flexible extension of the skew Laplace normal distribution which is also a heavy-tailed distribution. The SMSLN distribution includes an extra shape parameter, which controls skewness and kurtosis. Some distributional properties of this distribution are derived. Besides, we propose finite mixtures of SMSLN distribu- tions to model both skewness and heavy-tailedness in heterogeneous data sets. The maximum likelihood estimators for parameters of interests are obtained via the expec- tation–maximization algorithm. We also give a simulation study and examine a real data example for the numerical illustration of proposed estimators. Keywords EM algorithm · Finite mixture model · ML · SMSLN 1 Introduction Finite mixture models are a most popular analytical tool for modeling heterogeneous data sets which are used in many application areas such as classification, cluster and latent class analysis, density estimation, data mining, image analysis, pattern recog- nition, etc. [see for more detailed explanations, Titterington et al. (1985), McLachlan and Basford (1988), McLachlan and Peel (2000), Bishop (2006), Frühwirth-Schnatter (2006)]. In general, distributions of components are assumed to be normal since it has a comprehensive application area and ease of computation. In practice, it is not easy to find a data set, which behaves normally since the measured component den- B Fatma Zehra Do˘ gru fatma.dogru@giresun.edu.tr Olcay Arslan oarslan@ankara.edu.tr 1 Department of Statistics, Faculty of Arts and Sciences, Giresun University, 28200 Giresun, Turkey 2 Department of Statistics, Faculty of Science, Ankara University, 06100 Ankara, Turkey 123