A master’s thesis at the College of Management and Economics at the University of Karbala discussed the use of the spherical inverse method to estimate the survival function of the semicircular “Shanker” distribution, with a practical application.
The study presented by student Hanan Jassab Muhammad aimed to propose a new probability distribution using the spherical inverse formula to represent circular data, as well as deriving the circular characteristics of the distribution to obtain the best estimate of the survival function using the maximum potential method, the weighted least squares method, and the “Cramer-von Mises” method. This is done through the average statistical indicator.
The thesis concluded that the proposed probability distribution (Stereographic Semicircular Shankar) represents and describes the real data better than the “Shanker” distribution, which reflects the importance of the semicircular probability distribution compared to the original probability distribution.
The study recommended using the Cramer von Mises (CVM) method to estimate the parameters of the survival function of the Stereographic Semicircular distribution at small, medium, and large sample sizes, and the weighted least squares method at small and medium sample sizes.
