Far East Journal of Theoretical Statistics © 2015 Pushpa Publishing House, Allahabad, India Published Online: February 2016 http://dx.doi.org/10.17654/FJTSNov2015_119_128 Volume 51, Number 3, 2015, Pages 119-128 ISSN: 0972-0863 Received: August 19, 2015; Revised: October 9, 2015; Accepted: October 10, 2015 2010 Mathematics Subject Classification: 62H11. Keywords and phrases: chi square, semicircular, inverse stereographic projection, characteristic function. Communicated by Kuan-Fu Shen; Editor: Advances and Applications in Statistics: Published by Pushpa Publishing House. THE STEREOGRAPHIC SEMICIRCULAR CHI SQUARE MODELS Getut Pramesti Department of Mathematic Education Sebelas Maret University Surakarta, Indonesia e-mail: getutpramesti@staff.uns.ac.id Abstract The chi square distribution which is one particular form of the Gamma distribution can be applied in the actuarial field. In this paper, an inverse stereographic projection, from the real line to the semi-circle, is used as the background to construct stereographic semicircular chi square model theoretically. We proposed the trigonometric moments which is derived from the characteristic function. The characteristic function is used to evaluate the characteristics of population of the semicircular model such as the mean resultant length, mean direction, semicircular variance. 1. Introduction The development of research on directional statistics is very rapidly, but it can be seen that there is sparse research on the application in the actuarial field. One of the distributions which can be applied in the actuarial field