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

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  • Yann Dijoux

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.

Suggested Citation

  • Yann Dijoux, 2023. "A new class of distributions on the whole real line based on the continuous iteration approach," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(14), pages 4934-4959, July.
    • Handle: RePEc:taf:lstaxx:v:52:y:2023:i:14:p:4934-4959
    DOI: 10.1080/03610926.2021.1991376
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