Construction of the tetration distribution based on the continuous iteration of the exponential‐minus‐one function - Archive ouverte HAL Access content directly
Journal Articles Applied Stochastic Models in Business and Industry Year : 2020

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

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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.
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Dates and versions

hal-02560102 , version 1 (01-05-2020)

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Yann Dijoux. Construction of the tetration distribution based on the continuous iteration of the exponential‐minus‐one function. Applied Stochastic Models in Business and Industry, 2020, 36 (5), pp.891-916. ⟨10.1002/asmb.2538⟩. ⟨hal-02560102⟩
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