A half circular distribution for modeling the posterior corneal curvature

ABSTRACTThe posterior corneal curvature and many other medical, environmental, and ecological variables are measured with angles where its range is less than π. Such data are so-called axial or half circular data. Half circular data modeling has not received much attention from researchers. This paper proposes a new half circular distribution model based on inverse stereographic projection technique of Burr-XII distribution. The maximum likelihood estimates of parameters are obtained and a simulation study to evaluate the performance of estimates was carried out. The application on the posterior corneal curvature of 23 patients shows that the proposed distribution fits the data well.