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A new class of distributions on the whole real line based on the continuous iteration approach.
- Source :
-
Communications in Statistics: Theory & Methods . 2023, Vol. 52 Issue 14, p4934-4959. 26p. - Publication Year :
- 2023
-
Abstract
- The continuous iteration of an exponential-type function allows to describe a whole range of growths between logarithmical and exponential. This principle has been applied to a class of lifetime distributions called Tetration distribution and its subsequent tail has the property to belong to an extremely versatile family, from heavy-tailed to light-tailed. The present paper aims to construct a statistical distribution on the whole real line, based on the same principle. This new distribution, denoted Asymmetric Tetration distribution is obtained by combining a reflection of the Tetration distribution with skewing methods. Two inference methods are developed and compared in terms of performance of their estimators. In addition, an index of tail heaviness at − ∞ is proposed and computed for the most common distributions on the whole real line. Finally, the Asymmetric Tetration distribution is applied to data sets in the finance domain. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03610926
- Volume :
- 52
- Issue :
- 14
- Database :
- Academic Search Index
- Journal :
- Communications in Statistics: Theory & Methods
- Publication Type :
- Academic Journal
- Accession number :
- 163954384
- Full Text :
- https://doi.org/10.1080/03610926.2021.1991376