# A New Family of Asymmetric Distributions for Modeling Light-Tailed and Right-Skewed Data

## TL;DR

This paper introduces the generalized exponential log-squared (GEL-S) distribution, a new asymmetric, light-tailed distribution with flexible data fitting capabilities, supported by theoretical properties, simulations, and real data applications.

## Contribution

The paper presents a novel three-parameter distribution that models light-tailed, right-skewed data, distinct from existing distributions, with detailed statistical properties and estimation methods.

## Key findings

- GEL-S effectively fits light-tailed, right-skewed data.
- Simulation studies demonstrate the distribution's flexibility and estimation accuracy.
- Real data applications confirm its practical usefulness.

## 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.