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Construction of the tetration distribution based on the continuous iteration of the exponential‐minus‐one function

Construction of the tetration distribution based on the continuous iteration of the... A new class of lifetime distributions, called tetration distribution, is presented based on the continuous iteration of the exponential‐minus‐one function. In particular, this distribution encompasses and extends the Weibull, Pareto, and Gompertz distributions. In addition, a characterization of the tail of the distribution is proposed through two indices, one of them encompassing the Pareto and Weibull tail indices. Finally, an inference procedure based on rank regression is implemented for the tetration distribution and applied to multiple datasets from the reliability field. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Stochastic Models in Business and Industry Wiley

Construction of the tetration distribution based on the continuous iteration of the exponential‐minus‐one function

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References (44)

Publisher
Wiley
Copyright
© 2020 John Wiley & Sons, Ltd.
ISSN
1524-1904
eISSN
1526-4025
DOI
10.1002/asmb.2538
Publisher site
See Article on Publisher Site

Abstract

A new class of lifetime distributions, called tetration distribution, is presented based on the continuous iteration of the exponential‐minus‐one function. In particular, this distribution encompasses and extends the Weibull, Pareto, and Gompertz distributions. In addition, a characterization of the tail of the distribution is proposed through two indices, one of them encompassing the Pareto and Weibull tail indices. Finally, an inference procedure based on rank regression is implemented for the tetration distribution and applied to multiple datasets from the reliability field.

Journal

Applied Stochastic Models in Business and IndustryWiley

Published: Sep 1, 2020

Keywords: ; ; ; ; ;

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