Circular data arise in various walks of life, where we consider the unit circle to be the sample space. Minh &Farnum (2003) developed that Mobius transformation or Stereographic projection is applied to generate probability distributions on real line. We derive an asymmetric distribution called Stereographic Lognormal distribution to model circular data with an emphasis on the Inverse Stereographic Projection. The graphs of probability density function, cumulative distribution function and characteristic function are drawn. Since Stereographic Lognormal distribution is an asymmetric, a complex-valued characteristic function is derived and population characteristics are also studied. Goodness of fit is verified for the data Set of cross – bed azimuths of palaeocurrents of size 40 which contains angular data.

This paper introduces a novel semicircular distribution obtained by applying the quadratic rank transmutation map to the stereographic semicircular exponential distribution, referred to as the transmuted stereographic semicircular exponential distribution (TSSCED). This newly proposed distribution exhibits enhanced flexibility compared to the baseline stereographic semicircular exponential distribution (SSCEXP). We conduct a comprehensive analysis of the model’s properties and demonstrate its efficacy in data modeling through the application to a real dataset.

This paper introduces Stereographic Double Exponential Model based on inverse Stereographic Projection or Bilinear (Mobius) Transformation, [Minh and Farnum (2003)]. onsidering the data set of 13 homing pigeons were released singly in the Toggenburg Valley in Switzerland under sub Alpine conditions (data quoted in Batschelet (1981)), it is shown that the said model is a good fit by most of the tests at various level of significance. The derivation of the characteristic function for Stereographic Double Exponential Model and its trigonometric moments are presented. Relative performance of Stereographic Logistic [Phani (2013], Wrapped Logistic [Dattatreya Rao et al (2007)] and Stereographic Double Exponential models for the live data of 13 birds is studied. Also graphs of pdf of this new Model for various combinations of the parameters are drawn.

In this paper we make an attempt to construct a new three parameter linear model, we call this new model as Arc Tan-Exponential Type distribution, by applying Stereographic Projection or equivalently Bilinear transformation on Wrapped Exponential distribution, Probability density and cumulative distribution functions of this new model are presented and their graphs are plotted for various values of parameters.

In this paper, we obtain a Suzuki type unique common fixed point theorem using C-condition in partial metric spaces. In addition, we give an example which supports our main theorem.