Articles | Volume 12, issue 2
https://doi.org/10.5194/ascmo-12-211-2026
https://doi.org/10.5194/ascmo-12-211-2026
25 Aug 2026
 | 25 Aug 2026

On computing the maximum likelihood estimates for the q-Pareto distribution and application to earthquakes

Fatah Benatia and Mohammed Ridha Kouider

Cited articles

Balkema, A. A. and De Haan, L.: Residual life time at great age, Ann. Probab., 2, 792–804, 1974. 
de la Barra, E. and Vega-Jorquera, P.: On q-pareto distribution: some properties and application to earthquakes, Eur. Phys. J. B, 94, 32, https://doi.org/10.1140/epjb/s10051-021-00045-7, 2021. 
Kouider, M. R.: On Maximum Likelihood Estimates for the Shape Parameter of the Generalized Pareto Distribution, Science Journal of Applied Mathematics and Statistics, 7, 89–94, 2019a. 
Kouider, M. R.: Modified Bisection Algorithm for Multiple Roots of Nonlinear Equation With the R Software, SSRN Electronic Journal, https://doi.org/10.2139/ssrn.3451155, 2019b. 
Kouider, M. R. and Benatia, F.: Modified bisection algorithm in estimating the extreme value index, International Conference of Young Mathematicians – The Institute of Mathematics of the National Academy of Sciences of Ukraine, https://www.imath.kiev.ua/~young/youngconf2023/Abstracts_2023/PS/Kouider_Benatia.pdf (last access: 10 June 2023), 2023. 
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Short summary
The aim of this study is to develop efficient estimation methods of the maximum likelihood estimation method for the q-Pareto distribution (q-PD) parameters that are based on numerical methods to maximize the log-likelihood of the q-PD. And the q-PD parameters is a q-exponential distribution, finding applications in many fields such as:  seismology (earthquake patterns).
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