JMAT_V5_N1_RP4 Phani Yedlapalli S.V.S.Girija A.V. Dattatreya Rao Journal on Mathematics 2277-5137 5 1 39 46 Angular Data, Characteristic Function, Semicircular Model, Stereographic Double Exponential Distribution, Semicircular Laplace Distribution, Stereographic Projection, l-axial Data, Projection Trigonometric Moments Modeling of circular data with limited number of available circular models such as, von Mises, Wrapped Cauchy, Cardioid, etc., was done in various domains like Neuro Science, Geography, Archaeology, Remote Sensing, Spatial Analysis, Plant Phenology and Political Science. Dattatreya Rao (2007; 2011a;2011b;2011c; 2013a; 2013b; 2016) and Girija (2010; 2013a; 2013b; 2014a; 2014b), Phani (2012a; 2012b; 2013a; 2013; 2014; 2015a; 2015b; 2015c; 2015d), Radhika (2013a; 2013b; 2014;2015) and Devaraaj (2012; 2014) have introduced several new models and a few new methodologies of constructing the new circular models. These circular models are constructed by applying wrapping method, inverse stereographic projection, offsetting and the rising sun function. It is observed that, the simple projection method is not a much paid attention in constructing circular models. Glancing the literature, semicircular, arc and skewed angular data were observed in the applications and sufficient number of models for such data is not available. Motivated by these points, the authors have introduced semicircular reflected gamma distribution for modelling semicircular data by a simple projection method on reflected gamma distribution. The authors have extend it to the laxial reflected gamma distribution by a simple projection for modeling any arc of arbitrary length, and also the first four trigonometric moments has been derived for the proposed model. January - March 2016 Copyright © 2016 i-manager publications. All rights reserved. i-manager Publications http://www.imanagerpublications.com/Article.aspx?ArticleId=4870