Alternative skew Laplace scale mixtures for modeling data exhibiting high-peaked and heavy-tailed traits

Abstract

The search and construction of appropriate and flexible models for describing and modelling empirical data sets incongruent with normality retains a sustained interest. This paper focuses on proposing flexible skew Laplace scale mixture distributions to model these types of data sets. Each member of the collection of distributions is obtained by dividing the scale parameter of a conditional skew Laplace distribution by a purposefully chosen mixing random variable. Highly-peaked, heavy-tailed skew models with relevance and impact in different fields are obtained and investigated, and elegant sampling schemes to simulate from this collection of developed models are proposed. Finite mixtures consisting of the members of the skew Laplace scale mixture models are illustrated, further extending the flexibility of the distributions by being able to account for multimodality. The maximum likelihood estimates of the parameters for all the members of the developed models are described via a developed EM algorithm. Real-data examples highlight select models’ performance and emphasize their viability compared to other commonly considered candidates, and various goodness-of-fit measures are used to endorse the performance of the proposed models as reasonable and viable candidates for the practitioner. Finally, an outline is discussed for future work in the multivariate realm for these models.