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

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).