Title: A New Family of Asymmetric Distributions for Modeling Light-Tailed and Right-Skewed Data,
Abstract: A new three-parameter cumulative distribution function defined on
$(\alpha,\infty)$, for some $\alpha\geq0$, with asymmetric probability density
function and showing exponential decays at its both tails, is introduced. The
new distribution is near to familiar distributions like the gamma and
log-normal distributions, but this new one shows own elements and thus does not
generalize neither of these distributions. Hence, the new distribution
constitutes a new alternative to fit values showing light-tailed behaviors.
Further, this new distribution shows great flexibility to fit the bulk of data
by tuning some parameters. We refer to this new distribution as the generalized
exponential log-squared distribution (GEL-S). Statistical properties of the
GEL-S distribution are discussed. The maximum likelihood method is proposed for
estimating the model parameters, but incorporating adaptations in computational
procedures due to difficulties in the manipulation of the parameters. The
perfomance of the new distribution is studied using simulations. Applications
to real data sets coming from different domains are showed.