The exp-normal distribution is infinitely divisible

2018/03/06 by Iosif Pinelis, Pinelis, Iosif
Decision Sciences · Mathematics · #42A85 #62E10 #FOS: Mathematics #Primary 60E07 #Probability (math.PR) #Probability and Risk Models #Random Matrices and Applications #advanced mathematical theories #math.PR #msc:42A85 #msc:60E07 #msc:60E10 #msc:62E10 #secondary 60E10

paper · pdf · doi:10.48550/arxiv.1803.09838

3 pages

arxiv created 2018/03/06 · openalex publication_date 2018/03/06 · arxiv updated 2018/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Z be a standard normal random variable (r.v.). It is shown that the distribution of the r.v. ln|Z| is infinitely divisible; equivalently, the standard normal distribution considered as the distribution on the multiplicative group over ℝ∖\0\ is infinitely divisible.

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