Quasi-Exponentiated Normal Distributions: Mixture Representations and Asymmetrization
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 repr...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/17/3797 |
| _version_ | 1797582155816108032 |
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| author | Victor Korolev Alexander Zeifman |
| author_facet | Victor Korolev Alexander Zeifman |
| author_sort | Victor Korolev |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T23:18:02Z |
| format | Article |
| id | doaj.art-fc6c109b770f46a99ed95fa013b7a72c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T23:18:02Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-fc6c109b770f46a99ed95fa013b7a72c2023-11-19T08:32:17ZengMDPI AGMathematics2227-73902023-09-011117379710.3390/math11173797Quasi-Exponentiated Normal Distributions: Mixture Representations and AsymmetrizationVictor Korolev0Alexander Zeifman1Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Leninskie Gory, 119899 Moscow, RussiaFederal Research Center “Computer Sciences and Control” of the Russian Academy of Sciences, 44-2 Vavilova Str., 119333 Moscow, RussiaIn 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.https://www.mdpi.com/2227-7390/11/17/3797quasi-exponentiated normal distributionexponential power distributiongeneralized gamma distributionscale mixturelimit theoremrandom sum |
| spellingShingle | Victor Korolev Alexander Zeifman Quasi-Exponentiated Normal Distributions: Mixture Representations and Asymmetrization Mathematics quasi-exponentiated normal distribution exponential power distribution generalized gamma distribution scale mixture limit theorem random sum |
| title | Quasi-Exponentiated Normal Distributions: Mixture Representations and Asymmetrization |
| title_full | Quasi-Exponentiated Normal Distributions: Mixture Representations and Asymmetrization |
| title_fullStr | Quasi-Exponentiated Normal Distributions: Mixture Representations and Asymmetrization |
| title_full_unstemmed | Quasi-Exponentiated Normal Distributions: Mixture Representations and Asymmetrization |
| title_short | Quasi-Exponentiated Normal Distributions: Mixture Representations and Asymmetrization |
| title_sort | quasi exponentiated normal distributions mixture representations and asymmetrization |
| topic | quasi-exponentiated normal distribution exponential power distribution generalized gamma distribution scale mixture limit theorem random sum |
| url | https://www.mdpi.com/2227-7390/11/17/3797 |
| work_keys_str_mv | AT victorkorolev quasiexponentiatednormaldistributionsmixturerepresentationsandasymmetrization AT alexanderzeifman quasiexponentiatednormaldistributionsmixturerepresentationsandasymmetrization |