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- Title
Quasi-Exponentiated Normal Distributions: Mixture Representations and Asymmetrization.
- Authors
Korolev, Victor; Zeifman, Alexander
- 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.
- Subjects
LIMIT theorems; DISTRIBUTION (Probability theory); RANDOM numbers; GAUSSIAN distribution; RANDOM variables; INDEPENDENT variables; GAMMA distributions
- Publication
Mathematics (2227-7390), 2023, Vol 11, Issue 17, p3797
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math11173797