Skew Laplace candidates emanating from scale mixtures for insightful computational modelling

Abstract

The search for appropriate and flexible models for describing complex data sets, often with departure from normality, remains a main interest in various computational research fields. In this study, the focus is on developing flexible skew Laplace scale mixture distributions to model these 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 achieved. Finite mixtures consisting of the members of the skew Laplace scale mixture models are developed, further extending the flexibility of the distributions by being able to potentially account for multimodality. The maximum likelihood estimates of the parameters for all the members of the developed models are obtained via an EM algorithm. The models are fit to bodily injury claims of Massachusetts to show the applicability and compared to other existing flexible distributions. Various goodness of fit measures are used to validate the performance of the models as valid alternatives.