Work

Semicircular Maxwell–Boltzmann distribution: Application to posterior corneal curvature data

Year: 2025

Type: article

Abstract: The posterior corneal curvature is the shape of the rear part of the cornea which is the clear bulbous structure that covers the front of the human eyeball. This curvature has a significant bearing on the shape and structure of the entire eye. Since the elevation of the posterior cornea area is a precursor sign of keratoconus, it is crucial to assess the posterior corneal curvature in every patient undergoing LASIK surgery. In this paper, we present a semi-circular two-parameter model for posterior corneal curvature data called semi-circular Maxwell–Boltzmann distribution (SMBD) . The probability density function and mathematical properties of the proposed distribution are derived. The maximum likelihood estimation method is discussed for estimating the model’s parameters. Furthermore, a real-world application demonstrates that the SMBD provides superior fits than other popular circular distributions (CDs).

Source: Journal of Radiation Research and Applied Sciences

DOI: 10.1016/j.jrras.2025.101471

Authors: H.E. Semary, Alshad K.B., Jabir Bengalath, Safar M. Alghamdi

Institutions: Imam Mohammad ibn Saud Islamic University, Sri Ramachandra Institute of Higher Education and Research, University of Calicut, Taif University

Language: English

Topic: Statistical Distribution Estimation and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,400

Funders: Deanship of Scientific Research, Imam Mohammed Ibn Saud Islamic University, Al-Imam Muhammad Ibn Saud Islamic University