On Trigonometric Moments of the Stereographic Semicircular Gamma Distribution

Phani Yedlapalli, A.J.V.adhika Radhika, S.V.S Girija, A.V. Dattatreya Rao

Abstract

Phani (2013) constructed a good number of circular and semicircular models induced by inverse stereographic projection. Minh and Farnum (2003) and Toshihiro Abe et al (2010) proposed a new method to derive circular distributions from the existing linear models. In this paper, a new semicircular model, which is coined as Stereographic Semicircular Gamma distribution is derived by inducing modified inverse stereographic projection on Gamma distribution. This distribution generalizes Stereographic Semicircular Exponential model (Phani et al (2013)) and the density and distribution functions of proposed model admit closed form. Explicit expressions for trigonometric moments are derived by applying Meijer’s G- function and the new semicircular model is extended to construct Stereographic l- axial Gamma distribution.

Keywords

circular model, l- axial data, Meijer’s G- function, semicircular models, stereographic projection and trigonometric moments.

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