Inverse stereographic hyperbolic secant distribution: a new symmetric circular model by rotated bilinear transformations

The inverse stereographic projection (ISP), or equivalently, bilinear transformation, is a method to produce circular distribution based on an existing linear model. By the genesis of ISP method, many important models have been provided by researchers. In this study, we propose new symmetric unimodal/bimodal rotated considering hyperbolic secant as baseline distribution. Rotation means that fixing origin and rotating all other points same amount counterclockwise. Considering effect rotation be obtained with it seen actually induces location parameter in probability We analyze some stochastic properties proposed methods for estimation model simulation-based compare results these estimators are extensively paper. Furthermore, fitting performance according its well-known alternatives, such Von-Misses, wrapped Cauchy distributions, real data set. From information analysis data, say better than alternatives criteria frequently used literature.