Quasi-Exponentiated Normal Distributions: Mixture Representations and Asymmetrization

Victor Korolev () and Alexander Zeifman
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Victor Korolev: Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Leninskie Gory, 119899 Moscow, Russia
Alexander Zeifman: Federal Research Center “Computer Sciences and Control” of the Russian Academy of Sciences, 44-2 Vavilova Str., 119333 Moscow, Russia

Mathematics, 2023, vol. 11, issue 17, 1-14

Abstract: In the paper, quasi-exponentiated normal distributions are introduced for any real power (exponent) no less than two. With natural exponents, the quasi-exponentiated normal distributions coincide with the distributions of the corresponding powers of normal random variables with zero mean. Their representability as scale mixtures of normal and exponential distributions is proved. The mixing distributions are written out in the closed form. Two approaches to the construction of asymmetric quasi-exponentiated normal distributions are described. A limit theorem is proved for sums of a random number of independent random variables in which the asymmetric quasi-exponentiated normal distribution is the limit law.

Keywords: quasi-exponentiated normal distribution; exponential power distribution; generalized gamma distribution; scale mixture; limit theorem; random sum (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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