A novel stereographic semi-circular distribution and enhanced analysis of the posterior corneal curvature of eye
Year: 2024
Type: article
Abstract: Circular distributions articulate two-dimensional directions by mapping points onto a unit circle, vital in diverse fields such as medicine, ecology, and environmental studies which are measured in terms of angles. These often involve measuring angles within the (0, π) radians range, constituting axial or semi-circular data. This research seeks to introduce the Semi-Circular Marshall-Olkin extended Burr-XII distribution tailored for semi-circle datasets. Objectives encompass presenting its fundamental characteristics and applications. The inverse stereographic projection technique is applied for its development, deriving characteristics like trigonometric moments, mode, hazard function, and survival function. Six estimation techniques assess the distribution's parameters. Monte Carlo simulations evaluate parameter estimation methods for different sample sizes. Modeling the Semi-Circular Marshall-Olkin extended Burr-XII distribution with real-life semi-circle data of posterior corneal curvature of eye demonstrates its adaptability. Comparisons with existing distributions affirm its effectiveness. Extending to the l-axial model produces the Stereographic-l-axial MOE Burr-XII distribution, offering a distinct PDF. This transformation gives rise to specific scenarios and new models. The proposed Semi-Circular Marshall-Olkin extended Burr-XII distribution proves adept at handling real-world semi-circular data. The extension to the l-axial model and subsequent transformations introduces innovative models, demonstrated by superior compatibility in both circular and semi-circular datasets.
Source: Heliyon
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,100
Award: G875413501
OpenAlex ID: W4404514846