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Stereographic Logistic Model-Application to Noisy Scrub Birds Data

This paper introduces Stereographic Logistic Model based on inverse Stereographic Projection or Bilinear (Mobious) Transformation. Considering the data set of orientation of 50 noisy scrub birds along the bank of a creck bed, it is shown that the said model is a good fit using Watson’s U and Kuiper’s tests. The derivation of the characteristic function for Stereographic Logistic Model and its trigonometric moments are presented. Relative performance of Stereographic Logistic, Wrapped Logistic and Stereographic Double Exponential models for the live data of 50 noisy scrub birds is studied. Also graphs of pdf of this new Model for various combinations of the parameters are drawn. Here it is established that the new model is uni/bimodal depending on the concentration parameter, σ < 0.5 or σ > 0.5.