Yedlapalli, Phani; Radhika, A. J. V. Adhika; Girija, S. V. S.; Dattatreya Rao, A. V. On trigonometric moments of the stereographic semicircular gamma distribution. (English) Zbl 1388.60050 Eur. J. Pure Appl. Math. 10, No. 5, 1124-1134 (2017). Summary: Y. Phani [On stereographic circular and semicircular models. Namburu: Acharya Nagarjuna University (PhD Thesis) (2013)] constructed a good number of circular and semicircular models induced by inverse stereographic projection. D. Le Minh and N. R. Farnum [Commun. Stat., Theory Methods 32, No. 1, 1–9 (2003; Zbl 1025.62003)] and T. Abe et al. [“Symmetric unimodal models for directional data motivated by inverse stereographic projection”, J. Japan Statist. Soc. 40 No. 1, 45–61 (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 [P. Yedlapalli et al., J. Appl. Probab. Stat. 8, No. 1, 75–90 (2013; Zbl 1307.62145)] 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. Cited in 1 Document MSC: 60E05 Probability distributions: general theory 62H11 Directional data; spatial statistics Keywords:circular model; directional data; Meijer’s \(G\)-function; semicircular models; stereographic projection; trigonometric moments Citations:Zbl 1025.62003; Zbl 1307.62145 PDFBibTeX XMLCite \textit{P. Yedlapalli} et al., Eur. J. Pure Appl. Math. 10, No. 5, 1124--1134 (2017; Zbl 1388.60050) Full Text: Link