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

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  • Yann Dijoux

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.

Suggested Citation

  • Yann Dijoux, 2020. "Construction of the tetration distribution based on the continuous iteration of the exponential‐minus‐one function," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(5), pages 891-916, September.
    • Handle: RePEc:wly:apsmbi:v:36:y:2020:i:5:p:891-916
    DOI: 10.1002/asmb.2538
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    References listed on IDEAS

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    1. Stilian A. Stoev & George Michailidis, 2010. "On the estimation of the heavy‐tail exponent in time series using the max‐spectrum," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(3), pages 224-253, May.
    2. N. Balakrishnan & Debasis Kundu, 2019. "Birnbaum‐Saunders distribution: A review of models, analysis, and applications," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(1), pages 4-49, January.
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