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

Paper Details

Authors: Odat N.

DOI: 10.28924/2291-8639-24-2026-72

Journal: International Journal of Analysis and Applications

Year: 2026

Publisher: Etamaths Publishing

Document Type: Article

Open Access: All Open Access; Gold Open Access

Cited by: 1

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. © 2026 the author(s).

Keywords

Epanechnikov–Burr distribution; fixed point; Gauss–Seidel; iteration; maximum likelihood; non linrar operator

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