Gauss–Seidel Fixed-Point Approach for Maximum Likelihood Estimation in Epanechnikov–Burr XII Distributions

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DOI: https://doi.org/10.28924/2291-8639-24-2026-72
Published: Mar 12, 2026
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Naser Odat, Gauss–Seidel Fixed-Point Approach for Maximum Likelihood Estimation in Epanechnikov–Burr XII Distributions, Int. J. Anal. Appl., 24 (2026), 72.

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Naser Odat

Abstract

This paper introduces a Gauss–Seidel fixed-point iteration approach for estimating the parameters of the Epanechnikov–Burr XII distribution (EBD) probability density function using maximum likelihood principles. The proposed method updates the shape parameter θ and the scale parameter α in an alternating manner based on explicitly derived fixed-point equations. Numerical experiments are conducted to investigate the convergence behavior of the algorithm and to evaluate its performance in comparison with standard numerical optimization techniques.

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