Log-epsilon-skew normal: A generalization of the log-normal distribution. Issue 17 (1st September 2020)

• Record Type: Journal Article
• Authors: Hutson, Alan D.; Mashtare, Terry L.; Mudholkar, Govind S.
• Is Part Of: Communications in statistics. Volume 49:Issue 17(2020)
• Page Start: 4197
• Page End: 4215
• Publication Date: 2020-09-01
• Subjects: Hazard function -- log-normal distribution -- maximum likelihood estimation; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2019.1595655
• Languages: English
• ISSNs: 0361-0926

Abstract

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.