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Log-epsilon-skew normal: a generalization of the log-normal distribution. (English) Zbl 1511.62034

Summary: 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 G. S. Mudholkar and A. D. Hutson [J. Stat. Plann. Inference 83, No. 2, 291–309 (2000; Zbl 0943.62012)] 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.

MSC:

62E10 Characterization and structure theory of statistical distributions
60E05 Probability distributions: general theory
62F10 Point estimation

Citations:

Zbl 0943.62012
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References:

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