On Stereographic Lognormal Distribution

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.