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

Meitner Cadena

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arXiv · 1701.04880

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

Meitner Cadena

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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.

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Meitner Cadena. 2017-01-17. A New Family of Asymmetric Distributions for Modeling Light-Tailed and Right-Skewed Data. https://arxiv.org/abs/1701.04880

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