Fixed Point Maximum Likelihood Estimation for the Epanechnikov-Pareto Distribution

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DOI: https://doi.org/10.28924/2291-8639-23-2025-321
Published: Nov 28, 2025
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Anwar Bataihah, Naser Odat, Fixed Point Maximum Likelihood Estimation for the Epanechnikov-Pareto Distribution, Int. J. Anal. Appl., 23 (2025), 321.

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Anwar Bataihah, Naser Odat

Abstract

This paper develops a fixed-point iteration method for maximum likelihood estimation of the shape parameter θ in the Epanechnikov-Pareto Distribution (EPD). Building on Banach’s contraction principle, we establish a computationally efficient algorithm that reformulates the MLE problem as a fixed-point equation. Numerical simulations demonstrate rapid convergence within 6-10 iterations, reducing geometric error from 0.325 to 4.04×10−7. The proposed method significantly outperforms conventional optimization techniques, requiring only 18 iterations compared to 145 for Nelder-Mead while maintaining equivalent accuracy. Bootstrap validation with 500 replications confirms estimator stability, yielding a narrow 95% confidence interval [0.324015, 0.340532] with standard deviation 0.004148. The fixed-point approach provides a robust framework for parameter estimation in heavy-tailed distributions, with applications in reliability engineering and financial modeling.

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