Log-epsilon-skew normal: A generalization of the log-normal distribution

Commun Stat Theory Methods. 2020;49(17):4197-4215. doi: 10.1080/03610926.2019.1595655. Epub 2019 Mar 28.


The log-normal distribution is widely used to model non-negative data in many areas of applied research. In this paper, we introduce and study a family of distributions with non-negative reals as support and termed the log-epsilon-skew normal (LESN) which includes the log-normal distributions as a special case. It is related to the epsilon-skew normal developed in Mudholkar and Hutson (2000) the way the log-normal is related to the normal distribution. We study its main properties, hazard function, moments, skewness and kurtosis coefficients, and discuss maximum likelihood estimation of model parameters. We summarize the results of a simulation study to examine the behavior of the maximum likelihood estimates, and we illustrate the maximum likelihood estimation of the LESN distribution parameters to two real world data sets.

Keywords: Hazard function; distribution; likelihood estimation; log-normal; maximum.