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.
