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

Abstract

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
• log-normal distribution
• maximum likelihood estimation

Acknowledgments

The authors would like to thank Drs. Chris Andrews, Lili Tian, and Greg Wilding for reading the manuscript and providing helpful comments. We also would like to thank the reviewers for there careful comments, which led to a much improved revised version of this work.

Additional information

Funding

This work was supported by Roswell Park Cancer Institute and National Cancer Institute (NCI) grant P30CA016056, NRG Oncology Statistical and Data Management Center grant U10CA180822 and IOTN Moonshot grant U24CA232979-01.