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Construction of the tetration distribution based on the continuous iteration of the exponential‐minus‐one function
Author(s) -
Dijoux Yann
Publication year - 2020
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2538
Subject(s) - weibull distribution , mathematics , pareto principle , exponential function , exponential distribution , distribution fitting , distribution (mathematics) , lomax distribution , exponential family , exponentiated weibull distribution , statistics , mathematical analysis
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.