On computing the maximum likelihood estimates for the q -Pareto distribution and application to earthquakes
Year: 2026
Type: article
Abstract: We define a generalized exponential distribution ( G -ED) that overlaps with a generalized Pareto distribution (GPD). Then, we introduce the q -Pareto distribution ( q -PD) with two-parameter family distribution (strict positive shape and scale parameters) via transforming the G -ED. We demonstrate that the q -PD can be used to model the exceedances over a threshold, and we focus to estimate the q -PD parameters. Often, the estimation is taken the maximum likelihood estimation (MLE) because have a consistent estimator with an asymptotic normal distribution and is asymptotically effective in many cases. We present an algorithm to compute the MLE for q -PD parameters with confidence intervals for each estimator. Numerical examples are given to illustrate the results obtained. Efficient numerically methods are developed for the MLE of the q -PD parameters to maximize the log-likelihood of the q -PD.
Authors: Fatah Benatia, Mohammed Ridha Kouider
Institutions: University of Biskra, École Supérieure de la Sécurité Sociale
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7204179467