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

Yann Dijoux (1)

1 LM2S - Laboratoire Modélisation et Sûreté des Systèmes

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.

Mots clés: continuous iteration; extreme-value index; Gompertz distribution; Pareto distribution; tetration; Weibull distribution

Domaines: Recherche opérationnelle [math.OC]; Performance et fiabilité [cs.PF]

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⟩