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A new class of distributions on the whole real line based on the continuous iteration approach.

Authors :
Dijoux, Yann
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